Answer:
fair palybtgshsisuehdh
Two plastic bowling balls, 1 and 2, are rubbed with cloth until they each carry a uniformly distributed charge of magnitude 0.50 nC . Ball 1 is negatively charged, and ball 2 is positively charged. The balls are held apart by a 900-mm stick stuck through the holes so that it runs from the center of one ball to the center of the other.
Required:
What is the magnitude of the dipole moment of the arrangement?
Answer:
The right solution is "[tex]4.5\times 10^{-10} \ Cm[/tex]".
Explanation:
Given that,
q = 0.50 nC
d = 900 mm
As we know,
⇒ [tex]P=qd[/tex]
By putting the values, we get
⇒ [tex]=0.50\times 900[/tex]
⇒ [tex]=(0.50\times 10^{-9})\times 0.9[/tex]
⇒ [tex]=4.5\times 10^{-10} \ Cm[/tex]
Answer:
The dipole moment is 4.5 x 10^-10 Cm.
Explanation:
Charge on each ball, q = 0.5 nC
Length, L = 900 mm = 0.9 m
The dipole moment is defined as the product of either charge and the distance between them.
It is a vector quantity and the direction is from negative charge to the positive charge.
The dipole moment is
[tex]p = q L\\\\p = 0.5 \times 10^{-9}\times 0.9\\\\p = 4.5\times 10^{-10} Cm[/tex]
Part of your electrical load is a 60-W light that is on continuously. By what percentage can your energy consumption be reduced by turning this light off
Answer:
Following are the solution to the given question:
Explanation:
Please find the complete question in the attached file.
The cost after 30 days is 60 dollars. As energy remains constant, the cost per hour over 30 days will be decreased.
[tex]\to \frac{\$60}{\frac{30 \ days}{24\ hours}} = \$0.08 / kwh.[/tex]
Thus, [tex]\frac{\$0.08}{\$0.12} = 0.694 \ kW \times 0.694 \ kW \times 1000 = 694 \ W.[/tex]
The electricity used is continuously 694W over 30 days.
If just resistor loads (no reagents) were assumed,
[tex]\to I = \frac{P}{V}= \frac{694\ W}{120\ V} = 5.78\ A[/tex]
Energy usage reduction percentage = [tex](\frac{60\ W}{694\ W} \times 100\%)[/tex]
This bulb accounts for [tex]8.64\%[/tex] of the energy used, hence it saves when you switch it off.
Part C – RC Circuits in AC Mode 1. Derive Equation 5-6 from Equation 5-5. 2. Using the τ’s you calculated and your measured resistance: a. Calculate the capacitances of the capacitors. b. Compare your calculated and measured values via percent error.
Answer: hi your question is incomplete attached below is the complete question
1) attached below
2) a) 31 Ω, 302.9 Ω
b) 17.3 Ω , 26.4 Ω
Explanation:
1) Deriving Eqn 5-6 from Eqn 5-5
attached below
2) using τ’s calculated and measured resistance
use given data
Tm1 = Rm1 * Cm1
= 329.3 * 333 * 10^-9 = 109.65 μs
Tm2 = Rm2 * Cm2
= 329.3 * 200 * 10^-9 = 658.6 μs
a) Capacitance of capacitors
For Cm1
t₁₂ = 72 μs = R₁' Cm1 log²
∴ R₁' = ( 72 * 10^-6 ) / ( 333 * 10^-9 log² )
= 31 Ω
For Cm2
t₁₂ = 40 μs , ∴ R₂' = 302.9 Ω
b) comparing calculated and measured values via percent error
errors
Rm1 - R₁' = 17.3 Ω
Rm2 - R₂' = 26.4 Ω
The cart travels the track again and now experiences a constant tangential acceleration from point A to point C. The speeds of the cart are 10.6 ft/s at point A and 15.6 ft/s at point C. The cart takes 4.00 s to go from point A to point C, and the cart takes 1.80 s to go from point B to point C. What is the cart's speed at point B
Answer:
a) [tex]a_{avg}=1.25ft/s^2[/tex]
b) [tex]v_b=13.35ft/s[/tex]
Explanation:
From the question we are told that:
Speed at point A [tex]v_A=10.6ft/s[/tex]
Speed at point C [tex]v_C=15.6ft/s[/tex]
Time from Point A to C [tex]T_{ac}=4.00s[/tex]
Time from Point B to C [tex]T_{bc}=1.80s[/tex]
Generally the equation for acceleration From A to B is mathematically given by
[tex]a_{avg}=\frac{v_c-v_a}{\triangle t}[/tex]
[tex]a_{avg}=\frac{15.6-10.6}{4.0 }[/tex]
[tex]a_{avg}=1.25ft/s^2[/tex]
Generally the equation for cart speed at B is mathematically given by
[tex]a_{avg}=\frac{v_c-v_a}{T_{bc}}[/tex]
[tex]v_b=v_c-a_{avg}*T_{bc}[/tex]
[tex]v_b=15.6ft/s-(1.25ft/s^2)(1.80)[/tex]
[tex]v_b=13.35ft/s[/tex]
Can you think of reasons why the charge on each ball decreases over time and where the charges might go
Answer:
By the principle of corona discharge.
Explanation:
The charge on each ball will decreases over time due to the electrical discharge in air.
According to the principle of corona discharge, when the curvature is small, the discharge of the charge takes placed form the pointed ends.
The working substance of a certain Carnot engine is 1.90 of an ideal
monatomic gas. During the isothermal expansion portion of this engine's
cycle, the volume of the gas doubles, while during the adiabatic expansion
the volume increases by a factor of 5.7. The work output of the engine is
930 in each cycle.
Compute the temperatures of the two reservoirs between which this engine
operates.
Answer:
Explanation:
The energy for an isothermal expansion can be computed as:
[tex]\mathsf{Q_H =nRTIn (\dfrac{V_b}{V_a})}[/tex] --- (1)
However, we are being told that the volume of the gas is twice itself when undergoing adiabatic expansion. This implies that:
[tex]V_b = 2V_a[/tex]
Equation (1) can be written as:
[tex]\mathtt{Q_H = nRT_H In (2)}[/tex]
Also, in a Carnot engine, the efficiency can be computed as:
[tex]\mathtt{e = 1 - \dfrac{T_L}{T_H}}[/tex]
[tex]e = \dfrac{T_H-T_L}{T_H}[/tex]
In addition to that, for any heat engine, the efficiency e =[tex]\dfrac{W}{Q_H}[/tex]
relating the above two equations together, we have:
[tex]\dfrac{T_H-T_L}{T_H} = \dfrac{W}{Q_H}[/tex]
Making the work done (W) the subject:
[tex]W = Q_H \Big(\dfrac{T_H-T_L}{T_H} \Big)[/tex]
From equation (1):
[tex]\mathsf{W = nRT_HIn(2) \Big(\dfrac{T_H-T_L}{T_H} \Big)}[/tex]
[tex]\mathsf{W = nRIn(2) \Big(T_H-T_L} \Big)}[/tex]
If we consider the adiabatic expansion as well:
[tex]PV^y[/tex] = constant
i.e.
[tex]P_bV_b^y = P_cV_c^y[/tex]
From ideal gas PV = nRT
we can have:
[tex]\dfrac{nRT_H}{V_b}(V_b^y)= \dfrac{nRT_L}{V_c}(V_c^y)[/tex]
[tex]T_H = T_L \Big(\dfrac{V_c}{V_b}\Big)^{y-1}[/tex]
From the question, let us recall aw we are being informed that:
If the volumes changes by a factor = 5.7
Then, it implies that:
[tex]\Big(\dfrac{V_c}{V_b}\Big) = 5.7[/tex]
∴
[tex]T_H = T_L (5.7)^{y-1}[/tex]
In an ideal monoatomic gas [tex]\gamma = 1.6[/tex]
As such:
[tex]T_H = T_L (5.7)^{1.6-1}[/tex]
[tex]T_H = T_L (5.7)^{0.67}[/tex]
Replacing the value of [tex]T_H = T_L (5.7)^{0.67}[/tex] into equation [tex]\mathsf{W = nRIn(2) \Big(T_H-T_L} \Big)}[/tex]
[tex]\mathsf{W = nRT_L In(2) (5.7 ^{0.67 }-1}})[/tex]
From in the question:
W = 930 J and the moles = 1.90
using 8.314 as constant
Then:
[tex]\mathsf{930 = (1.90)(8.314)T_L In(2) (5.7 ^{0.67 }-1}})[/tex]
[tex]\mathsf{930 = 15.7966\times 1.5315 (T_L )})[/tex]
[tex]\mathsf{T_L= \dfrac{930 }{15.7966\times 1.5315}}[/tex]
[tex]\mathbf{T_L \simeq = 39 \ K}[/tex]
From [tex]T_H = T_L (5.7)^{0.67}[/tex]
[tex]\mathsf{T_H = 39 (5.7)^{0.67}}[/tex]
[tex]\mathbf{T_H \simeq 125K}[/tex]
Calculate the change in length of a 90.5 mm aluminum bar that has increased in temperature by from -14.4 oC to 154.6 oC
Take the coefficient of expansion to be 25 x 10-6 (oC)-1 . Write the answer in meters with three significant figures
Answer:
ΔL = 3.82 10⁻⁴ m
Explanation:
This is a thermal expansion exercise
ΔL = α L₀ ΔT
ΔT = T_f - T₀
where ΔL is the change in length and ΔT is the change in temperature
Let's reduce the length to SI units
L₀ = 90.5 mm (1m / 1000 mm) = 0.0905 m
let's calculate
ΔL = 25.10⁻⁶ 0.0905 (154.6 - (14.4))
ΔL = 3.8236 10⁻⁴ m
using the criterion of three significant figures
ΔL = 3.82 10⁻⁴ m
Suppose a power plant uses a Carnot engine to generate electricity, using the atmosphere at 300 K as the low-temperature reservoir. Suppose the power plant produces an amount of electric energy with the hot reservoir at 500 K during Day One and then produces the same amount of electric energy with the hot reservoir at 600 K during Day Two. The thermal pollution was:
Answer: hello your question lacks some vital information below is the complete question
Suppose a power plant uses a Carnot engine to generate electricity, using the atmosphere at 300 K as the low-temperature reservoir. Suppose the power plant produces 1 × 106 J of electricity with the hot reservoir at 500 K during Day One and then produces 1 × 106 J of electricity with the hot reservoir at 600 K during Day Two. The thermal pollution was
answer:
Total thermal pollution = 2.5 * 10^6 J
Explanation:
Low temperature reservoir = 300 K
hot reservoir temperature = 500 K
Electrical energy produced by plant ( W ) = 1 * 10^6 J
lets assume ; Q1 = energy absorbed , Q2 = energy emitted
W = Q1 - Q2 or Q2 = Q1 - W ( we will apply this as the formula for determining thermal pollution )
For day 1
T1 = 500k , T2 = 300k
applying Carnot engine formula
W / Q1 = 1 - T2/T1
∴ Q1 = 10^6 / ( 1 - (300/500)) = 2.5 * 10^6 J
thermal pollution ; Q2 = Q1 - W = ( 2.5 * 10^6 - 1 * 10^6 ) = 1.5 * 10^6 J
for Day 2
T1 = 600k, T2 = 300k
Q1 = 10^6 / ( 1 - (300/600)) = 2 * 10^6 J
Thermal pollution; Q2 = Q1 - W = 1 * 10^6 J
Therefore the Total thermal pollution = 1 * 10^6 + 1.5 * 10^6 = 2.5 * 10^6 J
How does the theory of relativity explain the gravity exerted by massive objects?
A. More massive objects create stronger forces of gravity.
B. More massive objects create shallower curves of space-time.
C. More massive objects pull objects from farther away.
D. More massive objects create larger curves of space-time.
(D)
Explanation:
The more massive an object is, the greater is the curvature that they produce on the space-time around it.
The theory of relativity explain the gravity exerted by massive objects is
more massive objects create larger curves of space-time (option-d).
Do bigger objects exert more gravity?The term "gravitational force" refers to the attraction between masses. The gravitational force increases in size as the masses get bigger (also called the gravity force). As the distance between masses grows, the gravitational force progressively lessens.
Greater gravitational forces will be used to attract heavier things since the gravitational force is directly proportional to the mass of both interacting objects. Therefore, when two things' respective masses increase, so does their gravitational pull to one another.
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Complete the following statement: The electromotive force is:______.a. the force that accelerates electrons through a wire when a battery is connected to it.b. the maximum potential difference between the terminals of a battery. c. the force that accelerates protons through a wire when a battery is connected to it.d. the maximum capacitance between the terminals of a battery.e. the potential difference between the terminals of a battery when the battery is not in use.
Answer:
The electromotive force is the maximum potential difference between the terminals of a battery.
The electromotive force is the maximum potential difference between the terminals of a battery. The correct option is b.
What is electromotive force?The electromotive force also called as EMF, is the force which causes current to flow from the positive to negative terminal of the battery.
The electromotive force is the maximum potential difference between the terminals of a battery.
Thus, the correct option is b.
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The earth's radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles as measured along the earth's surface.
a. Through what angle do you turn, relative to the earth, if you fly from Kampala to Singapore? Give your answer in both radians and degrees.
b. The flight from Kampala to Singapore take 9 hours. What is the plane's angular speed relative to the earth?
Answer:
a) the required angle in both radian and degree is 1.25 rad and 71.6°
b) the plane's angular speed relative to the earth is 3.86 × 10⁻⁵ rad/sec
Explanation:
Given the data in the question;
a)
we know that The expression for the angle subtended by an arc of circle at the center of the circle is,
θ = Length / radius
given that Length is 5000 miles and radius is 4000 miles
we substitute
θ = 5000 miles / 4000 miles
θ = 1.25 rad
Radian to Degree
θ = 1.25 rad × ( 180° / π rad )
θ = 71.6°
Therefore, required angle in both radian and degree is 1.25 rad and 71.6°
b)
The flight from Kampala to Singapore take 9 hours.
the plane's angular speed relative to the earth = ?
we know that, the relation between angular velocity and angular displacement is;
ω = θ / t
given that θ is 1.25 rads and time t is 9 hours or ( 9 × 3600 sec ) = 32400 sec
we substitute
ω = 1.25 rad / 32400 sec
ω = 3.86 × 10⁻⁵ rad/sec
Therefore, the plane's angular speed relative to the earth is 3.86 × 10⁻⁵ rad/sec
A flat coil of wire is placed in a uniform magnetic field that is in the y-direction.
The magnetic flux through the coil is maximum if the coil is:_________.
(a) in the XY plane
(b) in either the XY or the YZ plane
(c) in the XZ plane
(d) in any orientation, because it is constant.
Answer:
The correct answer is c
Explanation:
Flow is defined by
Ф = B . A
bold letters indicate vectors.
The magnetic field is directed to the y axis, The area of the coil is represented by a vector normal to the plane of the coil, so to have a flux
i.i = j.j = k.k = 1
and the tori scalar products are zero
a) If the coil must be in the xy plane so that its normal vector is in the Z axis, so there is no flux
b) if the coil is in the plane yz the normal veto is in the x axis, so the flux is zero
C) If the coil is in XZ, the normal vector points in the y direction, usually the scalar product is one and there is a flux in this configuration
The correct answer is c
A 300 kg block of dimensions 1.5 m × 1.0 m × 0.5 m lays on the table with its largest face.
Calculate:
Area of the largest face
Answer:
1.5
x 1.0
1.50
x 0.5
075.00
answer: 75.00m
Explanation:
I hope this help
At what rate must a cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.58 g
Answer:
w = 1,066 rad / s
Explanation:
For this exercise we use Newton's second law
F = m a
the centripetal acceleration is
a = w² r
indicate that the force is the mass of the body times the acceleration
F = m 0.58g = m 0.58 9.8
F = 5.684 m
we substitute
5.684 m = m w² r
w = [tex]\sqrt{5.684/r}[/tex]
To finish the calculation we must suppose a cylinder radius, suppose it has r = 5 m
w = [tex]\sqrt{ 5.684/5}[/tex]
w = 1,066 rad / s
A scientist who studies fossils of ancient life forms .O ornithologist O Paleontologist O Ichthyologist O Marine Biologist .
Hurry !! First one to answer gets points !
Answer:
paleontologist
Explanation:
Paleontologists are scientists that investigate the fossils of extinct life forms. Thus, the correct option is B.
What is Fossil?A fossil is defined as the preserved trace, imprint, or proof of a once-living entity from a past geological era. Exoskeletons, bones, shells, impressions of animals or microbes in stone, objects preserved in amber, hair, petrified wood, and genetic traces are a few examples. The collection of all the fossils is called as the fossil record.
An organism from a past geologic era that has been preserved in the Earth's crust is referred to as a fossil. Paleontologists are scientists that investigate the fossils of extinct life forms. The intricate system of fossil records is the main source of information about the evolution of life on Earth.
Therefore, the correct option is B.
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Two charged particles attract each other with a force of magnitude F acting on each. If the charge of one is doubled and the distance separating the particles is also doubled, the force acting on each of the two particles has magnitude
(a) F/2,
(b) F/4,
(c) F,
(d) 2F,
(e) 4F,
(f) None of the above.
Answer:
F/2
Explanation:
In the first case, the two charges are Q1 and Q2 and the distance between them is r. K is the Coulomb's constant
Hence;
F= KQ1Q2/r^2 ------(1)
Where the charge on Q1 is doubled and the distance separating the charges is also doubled;
F= K2Q1 Q2/(2r)^2
F2= 2KQ1Q2/4r^2 ----(2)
F2= F/2
Comparing (1) and (2)
The magnitude of force acting on each of the two particles is;
F= F/2
the speed of the pulse depends on what?
Answer:
The pulse speed depends on the properties of the medium and not on the amplitude or pulse length of the pulse.
Explanation:
Hope this helps.
Physical quantities expresed only by their magnitude is
Answer:
Scalar quantity is the Physical quantity expresed only by their magnitude.
Choose the force diagram that best represents a ball thrown upward by Peter, at the
top of its path.
Diagram A
Diagram B
Diagram C
Diagram D
Answer:Diagram A
Explanation:
Since the air resistance is to be neglected, only the gravitational force acts on the ball ( and has acted all the way from the throw upward). Diagram A reflects this fact correctly indicating the gravity acting on the ball downward.
In a certain cyclotron a proton moves in a circle of radius 0.530 m. The magnitude of the magnetic field is 1.30 T. (a) What is the oscillator frequency
Answer:
[tex]f=1.98\times 10^7\ Hz[/tex]
Explanation:
Given that,
The radius of circle, r = 0.53 m
The magnitude of the magnetic field, B = 1.3 T
We need to find the oscillator frequency. It is given by :
[tex]f=\dfrac{qB}{2\pi m}[/tex]
Put all the values,
[tex]f=\dfrac{1.6\times 10^{-19}\times 1.3}{2\pi \times 1.67\times 10^{-27}}\\\\f=1.98\times 10^7\ Hz[/tex]
So, the oscillator frequency is [tex]1.98\times 10^7\ Hz[/tex].
After de Broglie proposed the wave nature of matter, Davisson and Germer demonstrated the wavelike behavior of electrons by observing an interference pattern from electrons scattering off what
Answer:
Scattering is an interaction that can happen when a given particle or wave, like an electron, impacts a target or material. Then the electron changes it's original path and leaves some energy in the process. (This is a really simplified explanation of scattering, this is a really complex phenomenon, but let's not dive into that path)
Particularly, Davisson and Germer used a beam of electrons against a target of nickel, and these scattered electrons were detected by a detector. All of that in a vacuum chamber.
Then the correct answer is a nickel target.
"After de Broglie proposed the wave nature of matter, Davisson and Germer demonstrated the wavelike behavior of electrons by observing an interference pattern from electrons scattering off a nickel target"
A mixture of gaseous reactants is put into a cylinder, where a chemical reaction turns them into gaseous products. The cylinder has a piston that moves in or out, as necessary, to keep constant pressure on the mixture of 1 atm. The cylinder is also submerged in a large insulated water bath. The temperature of the water bath is monitored, and it is determined from this data that 133.0 kJ of heat flows into the system during the reaction. The position of the piston is also monitored, and it is determined from the data that the piston does 241.0 kJ of work on the system during the reaction.
a. Does the temperature of the water bath go up or down?
b. Does the piston move in or out?
c. Does heat flow into or out of the gaseous mixture?
d. How much heat flows?
What does Boyle's Law state about the relationship between the pressure and volume of an ideal gas at constant temperature?
a) The product of pressure and volume increases as pressure decreases.
b) The sum of pressure and volume is constant.
c) The sum of product and volume decreases as volume increases.
d) The product of pressure and volume is constant.
Answer:
Option (d).
Explanation:
According to the Boyle's law, for a given mass of a gas, the pressure of the gas is inversely proportional to the volume of the gas keeping the temperature of the gas is constant.
So,
Let the pressure is P, volume is V and T is the absolute temperature of the gas.
Pressure proportional to the reciprocal of the volume.
[tex]P \alpha \frac{1}{V}\\\\P V = constant[/tex]
The correct option is (d).
what is time taken by radio wave to go and return back from communication satellite to earth??
Answer:
Radio waves are used to carry satellite signals. These waves travel at 300,000 km/s (the speed of light). This means that a signal sent to a satellite 38,000 km away takes 0.13 s to reach the satellite and another 0.13 s for the return signal to be received back on Earth.
Explanation:
hope it help
Shooting a rock with a slingshot converts
energy to__________,
energy____________,
Answer:
converts elastic energy to mechanical energy
Explanation:
the magnitude of the magnetic field at point p for a certain electromagnetic wave is 2.21. What is the magnitude of the elctic field for that wave at P
Answer:
[tex]6.63\times 10^8\ N/C[/tex]
Explanation:
Given that,
The magnitude of magnetic field, B = 2.21
We need to find the magnitude of the electric field. Let it is E. So,
[tex]\dfrac{E}{B}=c\\\\E=Bc[/tex]
Put all the values,
[tex]E=2.21\times 3\times 10^8\\\\=6.63\times 10^8\ N/C[/tex]
So, the magnitude of the electric field is equal to [tex]6.63\times 10^8\ N/C[/tex].
A uniformly charged thin rod of length L and positive charge Q lies along the x-axis with its left end at the origin as shown in Figure 1.
a. Set up a correct integral expression for the potential at point A,which lies a distance H above the right end of the rod. Point A has coordinates (L, H). You need to give appropriate limits of integration and expressions for r and dq
b. Set up a correct integral expression for the potential at point B on the x-axis, a distance D from the left end of the rod with the appropriate limits of integration.You need to give appropriate limits of integration and expressions for r and dq.
Answer:
b)
Explanation:
How are elastic and inelastic collisions different?
A: Elastic collisions occur when the colliding objects move separately after the collision; after inelastic collisions, the objects are connected and move together.
B: Elastic collisions occur when the objects are going the same direction when they collide; inelastic collisions occur when the objects are going in opposite directions when they collide.
C: Momentum is conserved in elastic collisions; momentum is not conserved in inelastic collisions.
D: Elastic collisions occur between objects of the same mass; inelastic collisions occur between different masses.
Answer:
a
Explanation:
Answer:
the answer is c
'
Explanation:
Two spheres are rolling without slipping on a horizontal floor. They are made of different materials, but each has mass 5.00 kg and radius 0.120 m. For each the translational speed of the center of mass is 4.00 m/s. Sphere A is a uniform solid sphere and sphere B is a thin-walled, hollow sphere. Part B How much work, in joules, must be done on the solid sphere to bring it to rest? Express your answer in joules. VO AE4D ? J WA Request Answer Submit Part C How much work, in joules, must be done on the hollow sphere to bring it to rest? Express your answer in joules. Wa Request
Answer:
Explanation:
Moment of inertia of solid sphere = 2/5 m R²
m is mass and R is radius of sphere.
Putting the values
Moment of inertia of solid sphere I₁
Moment of inertia of hollow sphere I₂
Kinetic energy of solid sphere ( both linear and rotational )
= 1/2 ( m v² + I₁ ω²) [ ω is angular velocity of rotation ]
= 1/2 ( m v² + 2/5 m R² ω²)
= 1/2 ( m v² + 2/5 m v²)
=1/2 x 7 / 5 m v²
= 0.7 x 5 x 4² = 56 J .
This will be equal to work to be done to stop it.
Kinetic energy of hollow sphere ( both linear and rotational )
= 1/2 ( m v² + I₂ ω²) [ ω is angular velocity of rotation ]
= 1/2 ( m v² + 2/3 m R² ω²)
= 1/2 ( m v² + 2/3 m v²)
=1/2 x 5 / 3 m v²
= 0.833 x 5 x 4² = 66.64 J .
This will be equal to work to be done to stop it.
A 1500 kg car traveling at 20 m/s suddenly runs out of gas while approaching the valley shown in the figure. The alert driver immediately puts the car in neutral so that it will roll.
What will be the car’s speed as it coasts into the gas station on the other side of the valley?
Answer:
v_f = 17.4 m / s
Explanation:
For this exercise we can use conservation of energy
starting point. On the hill when running out of gas
Em₀ = K + U = ½ m v₀² + m g y₁
final point. Arriving at the gas station
Em_f = K + U = ½ m v_f ² + m g y₂
energy is conserved
Em₀ = Em_f
½ m v₀ ² + m g y₁ = ½ m v_f ² + m g y₂
v_f ² = v₀² + 2g (y₁ -y₂)
we calculate
v_f ² = 20² + 2 9.8 (10 -15)
v_f = √302
v_f = 17.4 m / s
