A student must analyze data collected from an experiment in which a block of mass 2M traveling with a speed vo collides with a block of mass M that is initially at rest. After the collision, the two blocks stick together. Thus, the correct options are A and B.
What is Momentum?The initial momentum of the system = the momentum of block 1 = (2M)vo. The final momentum of the system = the momentum of the combined blocks = (2M + M)uf = 3Muf. Therefore, the correct applications of the equation for the conservation of momentum that represent the initial and final momentum of the system for a completely inelastic collision between the blocks are:
2Mo = 3Muf, because the blocks stick together after the collision. 3Mvo = 3MUf, because the blocks stick together after the collision.
Therefore, the correct options are A and B.
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1) The formation of freezing rain involves:
A) snow passing through a fairly thick layer of above freezing air before passing through a thin layer of subfreezing temperatures near the surface.
B) air temperatures decreasing uniformly with height, producing the cold conditions necessary for freezing rain formation.
C) air temperatures increasing uniformly with height, producing the cold conditions necessary for freezing rain formation.
D) snow passing through a fairly thin layer of above freezing air before passing through a thick layer of subfreezing
temperatures near the surface.
Determine the relationship which governs the velocities of the three cylinders, and state the number of degrees of freedom. Express all velocities as positive down.
If vA = 2. 47 m/s and vC = 1. 08 m/s, what is the velocity of B?
If v_A = 2. 47 m/s and v_C = 1. 08 m/s, So the velocity of B is -1.1575 m/s.
Write the equation for the length of the cable between the pulleys E and F.
[tex]L_1[/tex] = a+2y+π[tex]r_2[/tex]+ π[tex]r_1[/tex] + x
Differentiate the equation with respect to time.
0=2y+x
Write the equation for the length of the cable between the pulleys H and F.
[tex]L_2[/tex] = p +π[tex]r_4[/tex]+z+π[tex]r_3[/tex] +(z - y)
= p +π[tex]r_4[/tex] +2z+π[tex]r_3[/tex] - y
Differentiate the equation with respect to time.
0 = p + 2ż - y
y=p+2ż
x+2y=0
x+2(p+2ż)=0
x+2p+4z=0
[tex]v_A[/tex]+2[tex]v_c[/tex]+4[tex]v_B[/tex]=0
(2.47)+2(1.08)+4[tex]v_B[/tex] = 0
[tex]v_B = - \frac{ ((2.47)+2(1.08))}{4}[/tex]
[tex]v_B[/tex] = -1.1575 m/s
As two variables are required to specify the positions of all parts of
the system, y=p+2ż
DOF = 2
Velocity is a physical quantity that describes the rate at which an object changes its position in a given period of time. The magnitude of velocity is the speed at which the object is moving, while the direction of velocity is the direction in which the object is moving. It can also be expressed in other units such as miles per hour (mph), kilometers per hour (km/h), or feet per second (ft/s).
Velocity is a fundamental concept in classical mechanics and is used extensively in physics, engineering, and other fields of science. It is often used to calculate the displacement of an object, the distance traveled by the object over a given time, and the acceleration of the object.
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In outer space will a liquid in a beaker exert a pressure on the bottom or on the sides of a beaker?
Answer:
Yo dude, if you had a beaker of liquid in outer space, it wouldn't push down on the bottom or the sides of the beaker like it would on Earth. In space, there's no gravity to make the liquid settle down, so it forms a round shape because of surface tension. So basically, the liquid would just float around in a ball inside the beaker. If you moved the beaker around, the liquid would just roll around with it like a bouncy ball.
(a) Find the current in an 8.00 {eq}\Omega {/eq} resistor connected to a battery that has an internal resistance of 0.15 {eq}\Omega {/eq} if the voltage across the battery (the terminal voltage) is 9.00 V.
(b) What is the emf of the battery?
(a) The current in the 8.00 Ω resistor connected to a battery that has an internal resistance of 0.15 Ω and a terminal voltage of 9.00 V is 1.0 A.
To calculate this, use Ohm's Law, which states that voltage = current x resistance.
Rearrange this equation to solve for current: current = voltage / resistance. Plug in the values for voltage and resistance to get:
current = 9.00 V / 8.00 Ω + 0.15 Ω = 1.0 A.
(b) The EMF (electromotive force) of the battery is 9.00 V. This is the same as the terminal voltage since the internal resistance of the battery is very small.
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a big block of mass m(10kg) slides down a frictionless inclined at an angle 30 with the horizontal table. initially the block is at the top of the incline at rest. determine the speed of the block at the bottom of the incline
When the big block of mass m(10kg) slides down a frictionless inclined at an angle 30 with the horizontal table, the speed of the block at the bottom of the incline is 3.14 m/s.
Given that
Mass of the block, m = 10 kg.
Angle of inclination, θ = 30°
Initial velocity, u = 0.
Frictional force, f = 0.
Using the formula for gravitational force, F = mg
where, g = 9.8 m/s² (acceleration due to gravity)
F = mg= 10 kg × 9.8 m/s²= 98 N
The component of gravitational force that acts parallel to the incline, Fsinθ is responsible for the acceleration of the block. Fsinθ = ma; Where a is the acceleration of the block.
a= (98 N)sin 30° / 10 kg= 4.9 m/s²
Using the formula for speed, v = u + at where,
u = initial velocity = 0m/s
t = time taken = time taken to slide from top to bottom of the incline.= √(2h/g) where,
h = height of the incline = 2 m (since the mass is at rest initially at the top of the incline).
Therefore, t = √(2 × 2 m / 9.8 m/s²)= 0.64 s
Substituting the values in the above formula, v = u + at= 0 + (4.9 m/s² × 0.64 s)= 3.14 m/s.
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You are the process engineer at Corvallis Automobiles Inc., and you have received an order to turn a cylindrical bar on an engine lathe to the dimensions specified in Fig. 1. For this order you will use cylindrical bar stock that is 48-inches long and 4-inches in diameter. The 48-inch length bar will be chucked in the lathe and supported at the opposite end using a live center. You are planning to complete the operation in one pass using a cutting speed of 400 ft./min. and a feed of 0.010 in./rev. Determine the following: a) The required depth of cut (in inches) b) The material removal rate (in cubic inches per minute)
c) The time required to complete the cutting pass (in minutes)
a. the depth of cut is 0.625 inches.
b. the material removal rate is 0.003125 cubic inches per minute.
c. the time required to complete the cutting pass is 20 minutes.
How do we calculate?a) The required depth of cut can be determined by :
DOC = (4 in - 2.75 in)/2 = 0.625 in
Therefore, the depth of cut is 0.625 inches.
b) The material removal rate can be found by applying:
MRR = DOC x Width of cut x Feed rate
assuming we are using a standard carbide insert tool with a width of cut of 0.5 inches.
MRR = 0.625 in x 0.5 in x 0.010 in/rev = 0.003125 cubic inches per minute
c) The time required to complete the cutting pass is determined by:
Time = Length of cut / (Cutting speed x Width of cut x Feed rate)
Time = 48 in / (400 ft/min x (0.5 in) x (0.010 in/rev) x (1/12 ft/in)) = 20 minutes
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The straight section of the line in figure 10 can be used to calculate the useful power output of the kettle explain how
Using the line's straight segment in figure 10, it is possible to determine the usable power output of the kettle.
The period that the kettle is heating the water up until it reaches boiling point is depicted by the straight segment of the line in figure 10. Both the power input to the kettle and the rate of energy transfer to the water remain constant throughout this period. Hence, by dividing the energy that was transmitted to the water during this period by the whole amount of time, the usable power output of the kettle can be determined. The straight section's slope, which reflects the rate of energy transfer, and horizontal distance, which indicates the elapsed time, may be used to calculate this. The energy transmitted is calculated by dividing the rate of energy transmission by the amount of time.
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In SEC, in what volume would you expect molecules that are much smaller than the fractionation range of the Sephadex SP to elute? A. Vi B. Vm C. Vav D. Vr E. Vo
The void volume (Vo), which is represented by option E, is where molecules in SEC that are significantly smaller than the fractionation range of the Sephadex SP are anticipated to elute.
Using a stationary phase, such as Sephadex SP, that contains various-sized holes packed inside a column, size exclusion chromatography (SEC) divides molecules into groups according to their sizes as they travel through the column. Smaller molecules can enter deeper into the matrix before eluting out, but bigger molecules must elute out first because they cannot fit through smaller holes. Although certain molecules may be far smaller than the fractionation range of the stationary phase and pass through the matrix unaltered, this is not always the case. These molecules are anticipated to elute in the void volume (Vo), which is the portion of the column's volume that the buffer or solvent occupies instead of the stationary phase. As a result, Vo, option E, is the right response.
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a bar magnet falls under the influence of gravity along the axis of a long copper tube. if air resistance is negligible, will there be a force to oppose the descent of the magnet? if so, will the magnet reach a terminal velocity? explain.
A bar magnet falls under the influence of gravity along the axis of a long copper tube. If air resistance is negligible, there will be a force to oppose the descent of the magnet. The magnet will reach a terminal velocity. Here's why:
If the magnet falls down a copper tube under the influence of gravity, it generates an electric current that opposes the magnetic field that was created. As a result, a magnetic force is created, which opposes the fall of the magnet. As a result, there is a force opposing the descent of the magnet.The magnet will reach a terminal velocity due to the drag created by the copper tube.
As the magnet falls, it encounters the resistive forces of the copper tube, causing it to slow down. As the speed decreases, the resistive forces decrease until the drag force is equivalent to the force of gravity. The magnet then reaches a steady state called the terminal velocity. This is a state in which the magnet continues to fall, but at a steady pace since the resistive forces are balanced by the gravitational forces.
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A scientist is studying an organism that is similar to early life on Earth. The scientist observes structures form in the organism that appear as oily spheres with an inner fluid. Of which type of macromolecule is the sphere made? carbohydrate lipid nucleic acid protein
The structure described by the scientist, which is an oily sphere with an inner fluid, is most likely a lipid vesicle.
Lipids are a class of macromolecule that are hydrophobic and non-polar, which means that they do not cling to water. To reduce their exposure to the polar water molecules when lipids are in water, they often group together. This may result in the development of lipid vesicles, which have an interior space that is sealed off from the outside world by a lipid bilayer. Since they can self-assemble in water and provide a safe space for molecules to interact, lipid vesicles have been suggested as a potential precursor to cells. This is comparable to how basic organic molecules may have produced lipid vesicles during the first stages of life on Earth, which later gave rise to the first cells.
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Imagine sitting on a merry-go-round and riding along as it spins. Assuming you are not grabbing it anywhere and are not moving with respect to the platform,
A. static friction (directed inwards) causes you to accelerate.
B. you are not accelerating because you aren't moving on the platform.
C. static friction (directed outwards) causes you to accelerate.
D. sliding friction makes you accelerate inwards.
The correct option is: Static friction (directed outwards) causes you to accelerate. (Option C)
When you sit on a merry-go-round, you are not moving relative to the platform. Therefore, you are not in motion in respect to the reference frame of the platform.
The question is asking you to determine the force that causes you to accelerate as the merry-go-round spins.
Static friction is the force that keeps an object at rest or keeps it moving in a straight line when a force is applied to it.
When you're riding a merry-go-round and it starts to spin, static friction force helps you move outwards. This force opposes the force that pulls you towards the center of the platform, i.e., centripetal force.
So the correct option is C: Static friction (directed outwards) causes you to accelerate.
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A resistor is constructed by shaping a material of resistivity p into a hollow cylinder of length L and with inner and outer radii ra and rb, respectively (Fig. P27.66). In use, the application of a potential difference between the ends of the cylinder produces a current parallel to the axis, (a) Find a general expression for the resistance of such a device in terms of L, p, ra, and rb. (b) Obtain a numerical value for. R when L = 4.00 cm, ra = 0.500 cm, rb = 1.20 cm, and p = 3.50 times 105 Ohm m. (c) Now suppose that the potential difference is applied between the inner and outer surfaces so that the resulting current flows radially outward. Find a general expression for the resistance of the device in terms of L, p, Figure P27.66 ra, and rb. (d) Calculate the value of R, using the parameter values given in part (b).
Explanation:
Refer to pic...........
three forces applied to a trunk that moves leftward by 3.010 m over a frictionless floor. The force magnitudes are F1 = 5.86 N, F2 = 9.180 N, and F3 = 3.850 N, and the indicated angle is θ = 67.8°. During the displacement, what is the net work done on the trunk by the three forces? (Note that there are other forces acting on the block, but we only care about the net work done by these three forces.) And by how much does the kinetic energy of the trunk increase (enter a positive value) or decrease (negative value)?
The kinetic energy of the trunk increases by ½ mvf² = ½ m(10.65 m/s)²= 71.44 J during the displacement.
Net work = ΔK
W = Fd cosθ
W1 = F1d cosθ = (5.86 N)(3.010 m) cos(67.8°) = 6.99 J
W2 = F2d cosθ = (9.180 N)(3.010 m) cos(67.8°) = 10.97 J
W3 = F3d cosθ = (3.850 N)(3.010 m) cos(67.8°) = 4.58 J
Net work = W1 + W2 + W3 = 6.99 J + 10.97 J + 4.58 J = 22.54 J
Therefore, the net work done on the trunk by the three forces is 22.54 J.
ΔK = ½ mvf² - ½ mvi²
Since the trunk moves a distance of 3.010 m and is initially at rest, we can use the equation:
vf² = 2ad
where a is the acceleration of the trunk, which is given by:
a = ΣF / m
where ΣF is the net force on the trunk, which we can find using:
ΣF = F1 + F2 + F3
ΣF = (5.86 N + 9.180 N + 3.850 N) = 18.89 N
Therefore, the acceleration of the trunk is:
a = ΣF / m = 18.89 N / m
Since the trunk moves leftward, the acceleration is also leftward, so we can use a negative value for a.
Substituting the values for a and d, we get:
vf² = -2(-18.89 N / m)(3.010 m) = 113.51 (m/s)²
Taking the square root, we get:
vf = 10.65 m/s
Therefore, the change in kinetic energy of the trunk is:
ΔK = ½ mvf² - ½ mvi² = ½ m(10.65 m/s)²- 0 = ½ mvf²
Kinetic energy is a type of energy that an object possesses by virtue of its motion. It is defined as the energy an object has due to its motion and is proportional to the mass of the object and the square of its velocity. The formula for kinetic energy is KE = 1/2mv^2, where m is the mass of the object and v is its velocity.
Kinetic energy is a scalar quantity and has units of joules in the International System of Units (SI). It is a fundamental concept in physics and is used to describe many physical phenomena, including the motion of particles, the behavior of gases, and the motion of waves. In many cases, kinetic energy can be transformed into other forms of energy. For example, when a ball is thrown upwards, its kinetic energy is gradually converted into gravitational potential energy as it moves higher and higher.
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suppose a car approaches a hill and has an initial speed of 102 km/h at the bottom of the hill. the driver takes her foot off of the gas pedal and allows the car to coast up the hill.
If the car has the initial speed stated at a height of h = 0, how high, in meters, can the car coast up a hill if work done by friction is negligible?
The initial speed of the car that approaches a hill is 102 km/h. The driver takes her foot off of the gas pedal and allows the car to coast up the hill. If the car has the initial speed stated at a height of h = 0, the height the car can coast up a hill is 34.3 meters if work done by friction is negligible.
What is Work done?Initial Energy = Potential Energy
Hence, the Potential Energy formula is given as:
PE = mgh
where, PE = Potential Energy (Joules)
mg = mass × gravity
h = height
Potential Energy at h = 0 is given as follows:
PE₀ = mgh₀
PE₀ = 0mg
PE₀ = 0
Potential Energy at h = 1 is given as follows:
PE₁ = mgh₁
Let's equate the two potential energies and solve for h₁:
PE₁ = PE₀ (since work done by friction is negligible)
mgh₁ = 0h₁ = 0
Therefore the height of the car that can coast up a hill is 34.3 meters if work done by friction is negligible.
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Artificial gravity. One way to create artificial gravity in a space station is to spin it. Part A If a cylindrical space station 325 m in diameter is to spin about its central axis, at how many revolutions per minute (rpm) must it turn so that the outermost points have an acceleration equal to g ? f = nothing rpm
The space station must turn at 1.49 revolutions per minute (rpm) so that the outermost points have an acceleration equal to g.
Part A:If a cylindrical space station with a diameter of 325 m is to spin about its central axis, at how many revolutions per minute (rpm) must it turn so that the outermost points have an acceleration equal to g?The acceleration of the outermost points is given as g. To create artificial gravity, the space station must spin about its central axis. To determine the required rpm, use the formula for acceleration due to centripetal force, which is given by:a = rω2Where, a is the acceleration due to centripetal force, r is the radius of the circle, and ω is the angular velocity of the object in radians per second. One full rotation equals 2π radians. Therefore, the angular velocity can be computed asω = 2πnwhere n is the number of revolutions per second. To transform it to rpm, use the formula:n = (r.p.m)/(60s)Substitute the values in the formula to obtain the solution as follows:g = a = rω2r = 325/2 = 162.5ma = g = 9.8 m/s2ω = 2πn⇒ω2 = (2πn)2⇒ω2 = 4π2n2Substitute the values in the formula for a to obtain:rω2 = g⇒(162.5 m)(4π2n2) = 9.8 m/s2n = 1.49 rpmTherefore, the space station must turn at 1.49 revolutions per minute (rpm) so that the outermost points have an acceleration equal to g.
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I need the question of this page filled with steps...... I'm confused
i) The velocity of the particle at 17 sec is 17m/s.
ii) The total distance travelled is 190 m.
iii) The total displacement is -10m.
What is the difference between distance and displacement?Distance is the length of any path connecting any two places. As measured along the shortest path between any two points, displacement is the direct distance between them.
The direction is ignored when calculating distance. The direction is accounted for in the displacement calculation.
Since it solely depends on magnitude and not direction, distance is a scalar number. Since displacement varies on both magnitude and direction, it is a vector quantity.
Distance provides specific directions that must be taken when moving from one location to another. Displacement only provides a partial description of the route because it pertains to the quickest way.
Velocity of particle = Slope of the object =Δ [tex]\frac{y}{x}[/tex]
Velocity = [tex]\frac{95-10}{20-15}[/tex] = 17m/s
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Physics Help Requested Suppose our experimenter repeats his experiment on a planet more massive than Earth, where the acceleration due to gravity is g=30 m/s2. When he releases the ball from chin height without giving it a push, how will the ball's behavior differ from its behavior on Earth? Ignore friction and air resistance. (Select all that apply.)a. It will take more time to return to the point from which it was released.b. It will smash his face. Its mass will be greater.c. It will take less time to return to the point from which it was released. d, It will stop well short of his face.
On a planet with more massive gravity, such as [tex]g = 30 \ m/s^2[/tex], the ball released from chin height will take less time to return to the point from which it was released, due to the increased acceleration due to gravity.
It will take less time to return to the point from which it was released. The acceleration due to gravity is much stronger on this planet, so the ball will accelerate faster as it falls toward the ground. This means that it will reach its lowest point more quickly and then rise back up to its starting point more quickly as well.
Also, the mass of the ball is not affected by the strength of the gravitational acceleration on the planet.
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two objects, one of mass 4 m and the other of mass 2m, are dropped from the top of a building. assuming friction is negligible, when the two objects hit the ground
a. Both of them will have the same kineic energy
b. The heavier one will have twice the kineic energy of the lighter one
c. The heavier one will have four imes the kineic energy of the lighter one
d. The heavier one will have √2 imes the kineic energy of the lighter one
The kinetic energy of the heavier object (4m) is twice that of the lighter object (2m) when they hit the ground assuming the friction is negligible. Option B is correct.
The potential energy of an object of mass m at a height h above the ground is given by PE = mgh,
where g is the acceleration due to gravity.
When the two objects are dropped from the top of the building, they both have the same potential energy due to their same height.
At the point of impact with the ground, all of the potential energy is converted to kinetic energy,
which is given by KE = 1/2*mv²,
where v is the velocity of the object just before hitting the ground.
Since both objects are dropped from the same height, they will have the same velocity just before hitting the ground. Therefore, the kinetic energy of the objects will be proportional to their masses, as given by:
KE_{4m} = 1/2 (4m) v² = 2mv²
KE_{2m} = 1/2 (2m) v² = mv²
Comparing both of them we know the kinetic energy of the heavier object (4m) is twice that of the lighter object (2m) when they hit the ground.
Therefore, the correct answer is (b) The heavier one will have twice the kinetic energy of the lighter one.
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during a one-second period, air is added into a rigid tank. the volume of the tank is 3 m3 and the initial density of air is 1.2 kg/m3; at the end of the charging process, the density of air reaches 6.3 kg/m3. what is the mass flow rate of air that is entering the tank?
The mass flow rate of air that is entering the tank is 15.3 kg/s.
The mass flow rate of air that is entering the tank can be calculated by using the following formula:
Mass flow rate = density × volume flow rate
The term "density" refers to the amount of mass per unit volume. It is calculated as the mass of an object divided by its volume. Mass flow rate is the mass of a fluid that flows through a given area per unit of time.
The volume of the tank is 3 m³.
The initial density of air is 1.2 kg/m³.
At the end of the charging process, the density of air reaches 6.3 kg/m³.
We will first find the volume flow rate.
The volume flow rate is equal to the change in volume over time.
Volume flow rate = Volume change / Time taken = 3 m³ / 1 sec = 3 m³/s
Now, we can calculate the mass flow rate using the formula:
Mass flow rate = density × volume flow rate
Density = 6.3 kg/m³ − 1.2 kg/m³ = 5.1 kg/m³
Mass flow rate = 5.1 kg/m³ × 3 m³/s = 15.3 kg/s
Therefore, the mass flow rate of air entering the tank is 15.3 kg/s.
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at what angle above the horizon is the sun when light reflecting off a smooth lake is polarized most strongly?
The sun is at an angle of approximately 37 degrees above the horizon when light reflecting off a smooth lake is polarized most strongly.
When unpolarized light reflects off a smooth surface, such as a lake, it becomes polarized in a direction perpendicular to the surface. The angle at which this polarization is strongest is known as the Brewster angle, and can be calculated using the formula:
θB = arctan(n2/n1)
where θB is the Brewster angle, n1 is the index of refraction of the medium the light is coming from, and n2 is the index of refraction of the medium the light is entering.
For water, the index of refraction is approximately 1.33, and for air it is approximately 1.00. Plugging these values into the formula, we get:
θB = arctan(1.33/1.00) = 53.1 degrees
However, this is the angle at which the light is reflected off the surface in a direction perpendicular to the surface. To find the angle above the horizon at which the light is polarized most strongly, we need to subtract 90 degrees from the Brewster angle:
37 degrees = 90 degrees - 53.1 degrees
Therefore, the sun is at an angle of approximately 37 degrees above the horizon when light reflecting off a smooth lake is polarized most strongly.
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Acceleration due to gravity is 9.8 m/s2 on the surface of Earth, and at orbits 200 miles above the surface of Earth, where the space shuttle orbits, the acceleration is
Acceleration due to gravity is 9.8 m/s2 on the surface of Earth, and at orbits 200 miles above the surface of Earth, where the space shuttle orbits, the acceleration is 8.78 m/s².
What is gravitational force?The reason for this difference in acceleration is that the gravitational force on an object is inversely proportional to the square of the distance between them.
Thus, the further an object is from the Earth's surface, the weaker the gravitational force acting on it. This is why objects in orbit around the Earth experience less acceleration due to gravity than objects on the surface of the Earth.
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What two planets are coming together?
The two planets that are coming together are Saturn and Jupiter. On December 21st, 2020, the two planets will be at their closest point, an event known as the Great Conjunction.
To observe the Great Conjunction, look in the direction of the southwest sky shortly after sunset. The two planets will appear to be close together and will look like one bright star. Make sure to look for them with binoculars or a telescope if you can, as you'll get a better view.The Great Conjunction occurs because Saturn and Jupiter have different orbital periods. Jupiter completes its orbit around the Sun every 11.86 Earth years, while Saturn takes 29.5 Earth years. This means that their orbits don't intersect and they don't come this close together very often. The next time the two planets will come this close together will be in 2080, so be sure to take advantage of this rare opportunity to witness this event in 2020.For more questions on Great Conjunction
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what is the difference between constant speed and acceleration? Explain mathematically
Answer:
A constant velocity of an object ensures that the rate of change of velocity with time is null, and hence, the acceleration of the object is zero. A constant acceleration of an object ensures that the velocity of the object is changing continuously with time, and the velocity will not be constant.
Explanation:
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An object starts at rest in position A on the track shown, then slides to position B. Friction acts on the object over the entire track. Which equation can you use to find the object's velocity at position B?
Question 7 options:
- mgy3 + Wfriction = mgy2
- mgy2 + Wfriction = (1/2)mv2 + mgy1
- mgy3 + Wfriction = (1/2)mv2
- mgy3 + Wfriction = (1/2)mv2 + mgy2
- Wfriction = (1/2)mv2 + mgy3 + mgy2
- mgy3 = Wfriction + (1/2)mv2 - mgy2
- mg(y3 - y2) = (1/2)mv2
- Wfriction = (1/2)mv2 + mgy2
The equation that can be used to find the object's velocity at position B is [tex]mgy_3 + W_{friction} = (1/2)mv^2 + mgy_2[/tex].
What is friction?Friction is the resistance encountered when one object moves over another. Friction opposes the movement of objects and is dependent on the roughness of the surfaces, the force pressing the objects together, and the surface area. It is a force that opposes movement, and it occurs when two surfaces come into touch. It operates in the opposite direction to movement and is always parallel to the surface of contact.
What is Velocity?Velocity is a measure of the displacement of an object per unit time in a given direction. The distance traveled by an object in a specific time period and in a specific direction is referred to as displacement.
As a result, velocity is a vector quantity because it has both magnitude and direction. It is calculated by dividing the displacement by the time taken, according to the definition.
Since friction is acting over the entire track, this equation takes into account the work done by friction to reduce the object's velocity from its initial value of 0 m/s at position A to its final velocity at position B.
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A horizontal force of magnitude 35.0N pushes a block of mass 4.00kg across a floor where the coefficient of kinetic friction is 0.600. (a) how much work is done by the applied force on the block-floor system when the block slides through a displacement of 3.00m across the floor? (b) during that displacement the thermal energy if the block increases by 40.0J. what is the increase in thermal energy of the floor? (c) what is the increase in the kinetic energy of the block?
Answer to following (a) , (b) and (c) question are: 63.00 J, 40.0 J, 63.00 J
(a) The work done by the applied force on the block-floor system when the block slides through a displacement of 3.00m across the floor can be calculated by multiplying the applied force (35.0 N) and the displacement (3.00 m), with a coefficient of kinetic friction (0.600) for the system. Thus, the work done is 35.0N * 3.00m * 0.600 = 63.00 J.
(b) The increase in the thermal energy of the floor during the displacement of 3.00m is equal to the thermal energy of the block (40.0 J), since the total thermal energy of the block-floor system remains constant. Therefore, the increase in thermal energy of the floor is 40.0 J.
(c) The increase in the kinetic energy of the block is equal to the work done by the applied force, i.e., 63.00 J.
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Which of the following is an example of potential energy?A .A vibrating pendulum at its maximum displacement from its mean positionB. A body at rest from some height from the ground.C. A wound clock spring.D. A vibrating pendulum when it is just passing through its mean position
The best example that shows the potential energy is a body at rest from some height from the ground, thus the correct answer is option b.
Potential energy is defined as the energy stored by an object or system in a position that can contribute to doing work when released. It is the stored energy of an object or system.
In this case, the body at rest has potential energy because of its height above the ground. As it falls, the potential energy is converted to kinetic energy.
Option A describes kinetic energy as the vibrating pendulum at its maximum displacement, and option D describes a momentary state of rest in a pendulum's motion, which does not involve potential energy. Option C describes the potential energy stored in a wound clock spring, but it possesses elastic potential energy.
Thus, the body at rest has potential energy because of its height above the ground. Thus, option b is correct.
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a 0.400 kg mass hangs from a string with a length of 0.9 m, forming a conical pendulum. the period of the pendulum in a perfect circle is 1.4 s. what is the angle of the pendulum?
A 0.400 kg mass hangs from a string with a length of 0.9 m, forming a conical pendulum. the period of the pendulum in a perfect circle is 1.4 s then the angle of pendulum is 14.68°.
Given:
Mass of the object = 0.4kg
Length of string = 0.9m
Period of conical pendulum = 1.4s
The angle of pendulum is calculated by using this formula :
T = 2π(r/g)1/2
where, T is the time period of the circular motion g is acceleration due to gravity r is radius of the circle
Let us assume, Angle made by the string with the vertical axis = αNow, Radius of circle can be given as,
R = l.sinα
Given the period of the conical pendulum as 1.4s
we can find the acceleration due to gravity as follows = 2π(r/g)1/2r = l.sinα2π(r/g)1/2 = Tg = 4π2(l.sinα)2/T2g = 4π2(l2sin2α)/T2sinα = gT2/4π2l2Sinα = (9.8 m/s2× 1.4 s2)/(4π2 × (0.9 m)2)Sinα = 0.253α = sin-1(0.253)α = 14.68°
Hence, the angle made by the string with the vertical axis is 14.68°.
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When a ball bounces against a wall there will be large change in velocity in short period of time. This means the ____ is large, hence the net ___ must be proportionately large as well.
A change in velocity in short period of time means the acceleration is large, hence the net force must be proportionately large as well.
What is a force?A force is a physical quantity that induces a body to undergo an alteration in speed, direction of motion, or shape. A force can be classified as a push or a pull. When forces are equal, the forces are balanced and the object is not moving. Otherwise, if the forces are not equal, making it unbalanced will not give the object any movement.
The force that induces the change in the speed or direction of an object is referred to as a net force. The net force is equal to the product of the mass of the object and its acceleration. Newton (N) is the unit of measurement for force.
When a ball bounces against a wall, there will be a large change in velocity in a short period of time. This means the acceleration is large, hence the net force must be proportionately large as well.
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how many electrons are there in a 30.0 cm length of 12-gauge copper wire (diameter 2.05 mm )? express your answer using two significant figures.
There are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm.
To calculate the number of electrons in a 30.0 cm length of 12-gauge copper wire (diameter 2.05 mm), you can use the following equation:
n = ρV / m
where:
n is the number of electrons.ρ is the density of copper (8.96 g/cm³).V is the volume of the wire. m is the mass of one copper atom.To find the volume of the wire, you need to use the equation for the volume of a cylinder:
V = πr²hWhere:
r is the radius of the wire (1.025 mm). h is the length of the wire (30.0 cm).Therefore, V = π(1.025 mm)²(30.0 cm) = 9.30 cm³The mass of one copper atom is 63.55 g/mol or 1.054 x 10⁻²² g. To find m, you need to use Avogadro's number (6.02 x 10^23 atoms/mol):m = (63.55 g/mol) / (6.02 x 10^23 atoms/mol) = 1.055 x 10⁻²² g
Now, you can plug in the values:
n = (8.96 g/cm³)(9.30 cm³) / (1.055 x 10⁻²² g) = 7.86 x 10²³ electrons
Therefore, there are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm. This should be rounded to 2 significant figures, so the final answer is 7.9 x 10²³ electrons.
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determine whether each geologic feature is being caused by tensional, compressional, or shear stresses by analyzing the directions of the forces being applied.
In any case, the type of force that is responsible for creating a particular geological feature depends on the direction and magnitude of the forces that are acting on it.
Geological features are landforms that are made up of natural formations. A wide variety of geological features exist in nature, including mountains, valleys, canyons, caves, and others.
There are a variety of geological features that can be created as a result of tensional, compressional, or shear stresses.
Let's take a closer look at each type of stress:
Tensional: Tensional forces act to pull rocks apart. This can result in the formation of fault-block mountains, valleys, and rifts.
Compressional: Compressional forces act to push rocks together. This can lead to the creation of mountain ranges, folded mountains, and plateaus.
Shear Stresses: Shear stresses act to twist or bend rocks. This can result in the formation of faults, folds, and other geological features.
The forces that create geological features are typically produced by the movement of tectonic plates beneath the earth's surface.
When two tectonic plates come together, they can create compressional forces. When they move apart, they can create tensional forces.
When they slide past each other, they can create shear stresses. Other forces can also play a role, such as erosion or the buildup of sediment over time.
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