The strength of the magnetic field is 0.16 T. This can be calculated using the formula: magnetic field strength (B) = force (F) / (current (I) × length (L) × sin(θ)),
where θ is the angle between the wire and the magnetic field (90 degrees in this case).
The formula to calculate the force on a current-carrying wire in a magnetic field is given by the equation: F = BILsin(θ), where F is the force, B is the magnetic field strength, I is the current, L is the length of the wire, and θ is the angle between the wire and the magnetic field.
Rearranging the formula, we get B = F / (ILsin(θ)).
Given:
Current (I) = 8.0 A
Length (L) = 0.50 m
Force (F) = 0.40 N
Angle (θ) = 90 degrees (since the wire is at right angles to the magnetic field)
Plugging in the values into the formula, we have:
B = 0.40 N / (8.0 A × 0.50 m × sin(90°)).
Since sin(90°) is equal to 1, the equation simplifies to:
B = 0.40 N / (8.0 A × 0.50 m × 1) = 0.16 T.
Therefore, the strength of the magnetic field is 0.16 T.
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A particle with a charge of 5nC has a distance of 0. 5m away from a charge of 9. 5nC. What is its electric potential energy?
The electric potential energy of the particle with a charge of 5nC, located 0.5m away from a charge of 9.5nC, is 1.9 J.
To calculate the electric potential energy, we can use the formula:
Electric potential energy = (k * q1 * q2) / r
Where:
k is the electrostatic constant (9 x 10^9 N m^2/C^2),
q1 and q2 are the charges of the two particles (in this case, 5nC and 9.5nC, respectively),
r is the distance between the charges (0.5m).
Substituting the given values into the formula:
Electric potential energy = (9 x 10^9 N m^2/C^2) * (5 x 10^-9 C) * (9.5 x 10^-9 C) / 0.5m
Calculating the expression:
Electric potential energy ≈ 1.9 J
Therefore, the electric potential energy of the particle is approximately 1.9 Joules.
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Inertia is the natural tendency of every object to resist change to either speed or direction. Describe a way in which you observe this in your everyday life.
Inertia refers to the natural tendency of every object to resist any change in either speed or direction. Every object tends to maintain its state of motion until an external force acts on it.
Inertia is an essential concept in physics, and it can be observed in everyday life. Here is how you can observe inertia in your everyday life:
When you are in a moving car, and the driver suddenly stops, your body tends to move forward. This is because of inertia. Your body is already in motion, and when the car stops, your body tends to keep moving in the same direction. The seatbelt helps to prevent this movement by exerting a force on your body in the opposite direction.
When you are on a merry-go-round and it starts spinning, you tend to feel a force pushing you away from the center of the ride. This is also due to inertia. Your body is already in motion, and when the ride starts spinning, your body tends to keep moving in the same direction. The force that pushes you away from the center of the ride is known as the centrifugal force.
When you are playing a game of pool, and you hit the cue ball, it tends to keep moving until it comes into contact with another ball or hits the wall of the table. This is also due to inertia. The cue ball is already in motion, and it tends to maintain its state of motion until it comes into contact with another object or hits the wall of the table.
These are just a few examples of how you can observe inertia in your everyday life.
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A 5-kg object is moving to the right at 4 m/s and collides with another object moving to the left at 5 m/s. The objects collide and stick together. After the collision, the combined object:
After the collision, the two objects stick together and move as one. Their total mass is m1 + m2 = 5 kg + m2.
How to determine the effect of the collisionIn this case, we can apply the principle of conservation of linear momentum
The initial momentum of the first object (P1_initial) is given by its mass (m1) times its velocity (v1), which is [tex]5 kg * 4 m/s = 20 kg*m/s.[/tex]
Therefore, the total initial momentum [tex](P_{total_initial}) is P1_{initial} + P2_{initial} = 20 kg*m/s - m2 * 5 m/s.[/tex]
After the collision, the two objects stick together and move as one.
Their total mass is m1 + m2 = 5 kg + m2.
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A 0. 10-kg ball traveling at 10 m/s hits a stationary wall and rebounds back with a velocity of 10 m/s. What is the impulse imparted by the wall?
The impulse imparted by the wall is -2 kg·m/s. The negative sign indicates a change in direction due to the rebound of the ball.
To determine the impulse imparted by the wall, we can use the principle of conservation of momentum. The impulse is equal to the change in momentum experienced by the ball.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Given:
Mass of the ball (m) = 0.10 kg
Initial velocity of the ball (v₁) = 10 m/s
Final velocity of the ball (v₂) = -10 m/s (negative sign indicates a change in direction)
The initial momentum of the ball is:
Initial momentum = m × v₁ = 0.10 kg × 10 m/s = 1 kg·m/s
The final momentum of the ball is:
Final momentum = m × v₂ = 0.10 kg × (-10 m/s) = -1 kg·m/s
The change in momentum is the difference between the final and initial momentum:
Change in momentum = Final momentum - Initial momentum = (-1 kg·m/s) - (1 kg·m/s) = -2 kg·m/s
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Driving a car 100m requires the same amount of _____ as pushing it 100m by hand. A. PowerB. Power and EnergyC. TimeD. Work
Driving a car 100m requires the same amount of work as pushing it 100m by hand as the concept of work in physics refers to the transfer of energy when a force is applied over a certain distance.
When driving a car or pushing it by hand, the same amount of work is done because the distance covered is the same. However, it's important to note that the power required to accomplish this work may differ, as power is the rate at which work is done or energy is transferred. So, while the work is the same, the power required for driving a car is typically much higher than the power needed to push it by hand.
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In the experiment, we measure the total time for 20 complete revolutions and divide it by 20 to obtain the period of the rotation. why not measure the amount of time for one complete revolution directly and record it as the period of rotation?
In the experiment, measuring the total time for 20 complete revolutions and dividing it by 20 to obtain the period of rotation is done to reduce errors and improve the accuracy of the measurement.
Measuring the time for one complete revolution directly can be subject to human reaction time and potential errors in starting and stopping the stopwatch precisely at the beginning and end of each revolution. These errors can accumulate and affect the accuracy of the measurement.
By measuring the total time for 20 complete revolutions and then dividing it by 20, we are essentially averaging out these potential errors over multiple revolutions. This helps to minimize the impact of any individual timing error and provides a more reliable and accurate measurement of the period of rotation.
Additionally, by taking multiple measurements (in this case, 20), we increase the sample size and reduce the influence of outliers or irregularities in any individual measurement. This improves the overall precision and reliability of the calculated period.
Therefore, measuring the total time for multiple revolutions and dividing by the number of revolutions allows for a more accurate determination of the period of rotation in the experiment.
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3. A grating with 1555 lines/cm is illuminated with light of wavelength 565 nm. What
is the highest-order number that can be observed with this grating? (Hint:
Remember that sin can never be greater than 1 for a diffraction grating. )
important!
The highest-order number that can be observed with this grating using diffraction formula is 1/1555.
It is determined using the formula for diffraction: mλ = d sinθ. Where m is the order number, λ is the wavelength of light, d is the grating spacing, and θ is the angle of diffraction. In this case, the grating has 1555 lines/cm, which means the grating spacing is 1/1555 cm.
To determine the highest-order number, calculate m × (565 × 10^-9 meters) = (1/1555 cm) × sinθ, where θ must be less than or equal to 90 degrees to satisfy sinθ ≤ 1. Given the wavelength of light as 565 nm (or 565 × 10^-9 meters), we can proceed with the calculation. Since sinθ ≤ 1, the highest-order number (m) can be determined by substituting θ = 90 degrees into the equation: m = (1/1555 cm) × sin(90 degrees).
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A bookshelf is at rest in a room. A force of 35. 0 newtons is applied to a bookshelf. If the floor imparts a frictional force of 2. 90 newtons, what is the net force acting on the bookshelf?.
The net force acting on the bookshelf is 32.1 N. It is given that the net force acting on a bookshelf that is at rest in a room when a force of 35.0 N is applied to it and the floor imparts a frictional force of 2.90 N.
The force that is applied to an object minus the frictional force acting on it is called net force. This net force is responsible for causing motion in the object. Therefore, if the object is at rest, the net force is zero. If it is in motion, the net force is nonzero.
The formula for calculating net force is: Net force = Applied force - Frictional force
Given: Applied force = 35.0 N, Frictional force = 2.90 N
We know that, Net force = Applied force - Frictional force
= 35.0 N - 2.90 N
= 32.1 N
Therefore, the net force acting on the bookshelf is 32.1 N.
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An elastic wire expands by 2cm when load of 40g hangs from it. What additional load will be required to cause a further extension of 4cm
Susie estimated that she can run for hours at a steady rate of 8mph. She enters a marathon, a distance of 26miles. How long should it take her to complete the race? Give answers in hours and minutes.
To determine the time it would take Susie to complete the marathon, we can use the formula: Time = Distance / Speed
Given that the distance of the marathon is 26 miles and Susie's steady rate is 8 mph, we can substitute these values into the formula. Time = 26 miles / 8 mph. To calculate the time, we divide 26 miles by 8 mph: Time = 3.25 hours. Since there are 60 minutes in an hour, we can convert the decimal part of the time to minutes: 0.25 hours * 60 minutes/hour = 15 minutes. Therefore, it would take Susie approximately 3 hours and 15 minutes to complete the marathon.
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A projectile is launched horizontally from a height of 8. 0 m. The projectile travels 6. 5 m before hitting the ground. The velocity of the projectile the moment it was launched, rounded to the nearest hundredth, is m/s.
The initial velocity of a projectile launched horizontally can be calculated using the equation of distance covered horizontally (x) = Initial velocity (u) Time of flight (t). The horizontal component of the initial velocity can be determined by x = u t, t = 1.63 s, x = 6.5 mu = x / t = 6.5 m / 1.63 su = 3.99 m/s 4.00 m/s.
The initial velocity of the projectile that was launched horizontally can be calculated using the equation below: Distance covered horizontally (x) = Initial velocity (u) × Time of flight (t) where, Time of flight (t) can be found using the formula below: t = [2 × vertical height (h)] / g where ,g is the acceleration due to gravity = 9.8 m/s².The vertical height (h) of the projectile is 8.0 m. So the time of flight of the projectile will bet = [2 × 8.0 m] / 9.8 m/s²t = 1.63 s Therefore, the horizontal component of the projectile’s initial velocity can be determined by: x = u × tt = 1.63 s, x = 6.5 mu = x / t = 6.5 m / 1.63 su = 3.99 m/s ≈ 4.00 m/s. So, the projectile was launched horizontally with a velocity of 4.00 m/s (rounded to the nearest hundredth).Content loaded: The term “content loaded” is used to indicate that the contents of a webpage or app have finished loading and are ready for viewing or use.
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The electron and proton of a hydrogen atom are separated by a distance of approximately 5.3 x 10^-11m. Find the magnitude of the electric and gravitational force between the two particles.
The magnitude of the electric force is 8.21 × 10⁻⁸ N and the gravitational force is 3.61 × 10⁻⁸ N. The electric force acting between the electron and proton of hydrogen atom is given by: Coulomb's Law of electrostatics, F = 1 / 4πε₀ × q₁q₂ / r².
Given that, Distance between the electron and proton of a hydrogen atom, r = 5.3 × 10⁻¹¹m, Mass of an electron, m₁ = 9.1 × 10⁻³¹ kg, Mass of a proton, m₂ = 1.67 × 10⁻²⁷ kg, Charge of an electron, q₁ = -1.6 × 10⁻¹⁹ C, Charge of a proton, q₂ = +1.6 × 10⁻¹⁹ C.
Where,ε₀ = permittivity of free space = 8.854 × 10⁻¹² C²/N m²
F = 1 / 4π (8.854 × 10⁻¹²) × (1.6 × 10⁻¹⁹)² / (5.3 × 10⁻¹¹)²
F = 8.21 × 10⁻⁸ N
The gravitational force acting between the electron and proton of hydrogen atom is given by:
Newton's Law of gravitation, F = G × m₁m₂ / r², Where, G = gravitational constant = 6.67 × 10⁻¹¹ N m²/kg²
F = (6.67 × 10⁻¹¹) × (9.1 × 10⁻³¹) × (1.67 × 10⁻²⁷) / (5.3 × 10⁻¹¹)²
F = 3.61 × 10⁻⁸ N
Therefore, the magnitude of the electric force is 8.21 × 10⁻⁸ N and the gravitational force is 3.61 × 10⁻⁸ N.
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A 20. Kilogram rock is lifted 7. 0 meters above the ground. What is the gravitational
potential energy of the rock?
The gravitational potential energy of the rock is 1,372 Joules.
The gravitational potential energy (PE) of an object can be calculated using the formula:
PE = m * g * h, where:
m is the mass of the object,
g is the acceleration due to gravity, and
h is the height or distance above the reference point.
In this case, the mass of the rock (m) is 20 kilograms, and the height (h) is 7.0 meters.
The acceleration due to gravity (g) is approximately 9.8 m/s².
Now we can calculate the gravitational potential energy:
PE = 20 kg * 9.8 m/s² * 7.0 m
PE = 1,372 Joules
Therefore, the gravitational potential energy of the rock is 1,372 Joules.
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Steam burns are pretty dangerous because there's often a lot of
thermal energy in the steam. When the steam hits you, it is going to
transfer some of that energy to you, cooling the steam. If a 6.4 kg cloud of
steam at 150 degrees, hits you and cools to 100 degrees, What is the loss
of heat energy? (no scientific notation)
The loss of heat energy when a 6.4 kg cloud of steam at 150 degrees Celsius hits you and cools to 100 degrees Celsius is 13,440,000 Joules.
To calculate the heat energy loss, we can use the formula:
Q = mcΔT
Where Q represents heat energy, m is the mass of the steam cloud (6.4 kg), c is the specific heat capacity of water (4,186 J/kg°C), and ΔT is the change in temperature (150°C - 100°C = 50°C).
Plugging in the values, we have:
Q = (6.4 kg) × (4,186 J/kg°C) × (50°C)
Q = 13,440,000 Joules
Therefore, the loss of heat energy when the steam cools from 150°C to 100°C is 13,440,000 Joules.
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A web browser is open on yur screen. The lengh of the monitor is x+7. The area of the browser windw is 24 inches. The dimensions of the browser window are x-2 and x. Find the length of the browser window x. Part B. The browser covers 3/13 of the screen. What are the dimensions of the screen
The length of the browser window (x) is 6. The dimensions of the screen are approximately 3 inches (width) and 18/13 inches (height).
Let's solve the equations step by step:
Part A:
The area of the browser window is given by the equation:
(x - 2) * x = 24
Expanding the equation:
[tex]x^{2}[/tex] - 2x = 24
Rearranging the equation to standard quadratic form:
[tex]x^{2}[/tex] - 2x - 24 = 0
Factoring the quadratic equation:
(x - 6)(x + 4) = 0
Setting each factor to zero:
x - 6 = 0 or x + 4 = 0
Solving for x:
x = 6 or x = -4
Since the length of the monitor cannot be negative, we discard the solution x = -4.
Therefore, the length of the browser window (x) is 6.
Part B:
The dimensions of the screen can be calculated using the length of the monitor (x+7) and the coverage ratio of the browser window (3/13).
The width of the screen is given by:
Width = (3/13) * (x + 7)
The height of the screen is given by:
Height = (3/13) * (x)
Substituting the value of x = 6:
Width = (3/13) * (6 + 7) = (3/13) * 13 = 3
Height = (3/13) * 6 = 18/13
Therefore, the dimensions of the screen are approximately 3 inches (width) and 18/13 inches (height).
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What is the approximate wavelength of a light whose second-order dark band forms a diffraction angle of 15. 0° when it passes through a diffraction grating that has 250. 0 lines per mm? 26 nm 32 nm 414 nm 518 nm.
To find the approximate wavelength of the light, we can use the formula:
wavelength (λ) = (d * sin(θ)) / m
where d is the spacing between the lines of the diffraction grating, θ is the angle of diffraction, and m is the order of the dark band.
In this case, the diffraction grating has 250.0 lines per mm, which means the spacing between the lines is:
d = 1 / 250.0 mm
The second-order dark band has an angle of diffraction of 15.0°, and we want to find the wavelength. So we can plug these values into the formula:
wavelength (λ) = [(1 / 250.0 mm) * sin(15.0°)] / 2
Calculating this expression gives us:
wavelength (λ) ≈ 32 nm
Therefore, the approximate wavelength of the light is 32 nm.
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Veronica’s velocity was measured as 4. 3 m/s. She displaced 20 meters in 4. 7 seconds. Which piece of information is missing for the correct calculation of velocity?
The missing piece of information required for the correct calculation of velocity is the direction of the displacement.
In order to calculate velocity accurately, we need to have both the displacement and the time. In this scenario, the displacement of 20 meters in 4.7 seconds is provided, but the missing piece of information is the direction of the displacement. Velocity is a vector quantity, which means it includes both magnitude (speed) and direction. To calculate the velocity accurately, we need to know whether Veronica's displacement was in a specific direction (e.g., north, east, etc.) or if it was only given as a magnitude (20 meters) without a direction.
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In a game of pool, a 0. 4 kg cue ball is traveling at 0. 80 m/s when it hits a slower striped ball moving at 0. 38 m/s. After the collision, the striped ball moves off at 0. 62 m/s. What is the magnitude of the final velocity of the cue ball? Assume all pool balls have the same mass. 0. 20 m/s 0. 56 m/s 1. 0 m/s 1. 8 m/s.
When solving the problem of pool game and calculating the magnitude of the final velocity of the cue ball, the correct option is 0.56 m/s.
The following method: Use the principle of conservation of momentum, i.e. momentum before the collision is equal to the momentum after the collision, which is mathematically written as: [tex]$$mv_1+Mv_2=(m + M)v_3$$[/tex]
Where, m is the mass of the cue ball,
M is the mass of the striped ball,
v1 is the velocity of the cue ball before the collision,
v2 is the velocity of the striped ball before the collision, and
v3 is the velocity of the cue ball after the collision.
Using the above formula, we get the final velocity of the cue ball as:
[tex]$$v_3=frac {mv_1+Mv_2}{m+M}$$[/tex]
Plug in the given values, we get,
[tex]$$v_3=frac{0.4*0.80+0.4*0.38}{0.4+0.4}$$[/tex]
Solving for v3, we get [tex]$v_3=0.59$[/tex] m/s Therefore, the magnitude of the final velocity of the cue ball is 0.59 m/s.
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Assuming a constant density, the size of an object scales as its mass raised to what power?.
Assuming a constant density, the size of an object scales as its mass raised to the power of 1/3 (one-third).
The mass, density, and volume of an object are related by the equation:
ρ = m/Vwhere ρ is the density, m is the mass, and V is the volume.
We can write this equation as
V = m/ρThis equation can be used to find the relationship between the mass and volume of an object of constant density.
Assume that we have two objects of the same material with masses m1 and m2.
We can find the ratio of their volumes by taking the ratio of their masses and density as follows:
V1/V2 = m1/ρ / m2/ρV1/V2 = m1/m2V1/V2 = (m1/m2)^(1/3)
This shows that the ratio of the volumes of two objects with the same density is proportional to the cube root of the ratio of their masses.
This relationship can be expressed as:
V ∝ m^(1/3)
This relationship can also be expressed as the size of an object scales as its mass raised to the power of 1/3.
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A stevedore slides a crate along a dock with a 50 kg horizontal force of 175 N. The opposing force of friction is 120 N. If started from rest, what is the crates’s final velocity after 0.5s?
To determine the crate's final velocity after 0.5 seconds, we can use the concept of Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this scenario, the stevedore applies a horizontal force of 175 N to move the crate along the dock. However, there is also an opposing force of friction acting in the opposite direction, which has a magnitude of 120 N. The net force is the difference between these two forces, so we can calculate it as follows:
Net force = Applied force - Frictional force
Net force = 175 N - 120 N
Net force = 55 N
Now, using Newton's second law of motion, we can determine the acceleration of the crate. Rearranging the equation, we have:
Net force = mass * acceleration
55 N = 50 kg * acceleration
Solving for acceleration:
acceleration = 55 N / 50 kg
acceleration = 1.1 m/s²
Since we know the initial velocity of the crate is zero (as it starts from rest), and we want to find the final velocity after 0.5 seconds, we can use the equation of motion:
final velocity = initial velocity + (acceleration * time)
Plugging in the values:
final velocity = 0 + (1.1 m/s² * 0.5 s)
final velocity = 0.55 m/s
Therefore, the crate's final velocity after 0.5 seconds is 0.55 m/s. This means that after being subjected to a 175 N force and experiencing 120 N of friction, the crate gains a velocity of 0.55 m/s in the direction of the applied force.
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A force of 25 N is applied to a screwdriver to pry the lid off of a can of paint. The screwdriver applies 75 N of force to the lid. What is the mechanical advantage of the screwdriver?
Answer:
The mechanical advantage of the screwdriver is 3.
Explanation:
The mechanical advantage can be calculated using the formula: mechanical advantage = output force / input force. In this case, the output force is 75 N (the force applied by the screwdriver to the lid), and the input force is 25 N (the force applied to the screwdriver).
Therefore, the mechanical advantage is:
mechanical advantage = 75 N / 25 N = 3.
Hence, the mechanical advantage of the screwdriver is 3.
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What is the energy of a wave that has a frequency of 9. 50 x 10^12 Hz?
The energy of the wave with a frequency of 9.50 x 10^12 Hz is approximately 6.2947 x 10^-21 Joules.
The energy of a wave can be calculated using the equation E = h*f, where E represents the energy, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and f is the frequency of the wave.
Given a frequency of 9.50 x 10^12 Hz, we can substitute this value into the equation to find the energy:
E = (6.626 x 10^-34 J·s) * (9.50 x 10^12 Hz)
E = 6.2947 x 10^-21 J
Therefore, the energy of the wave with a frequency of 9.50 x 10^12 Hz is approximately 6.2947 x 10^-21 Joules.
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A call can supply circuit of 0. 4A and 0. 2A through a 4ohms and 10 ohms resistor respectively what is the internal resistant of the cell
A call can supply circuit of 0. 4A and 0. 2A through a 4ohms and 10 ohms resistor respectively what is the internal resistant of the cellThe internal resistance of the cell is 3 ohms.
According to Ohm's Law, the current in a circuit can be determined using the equation I = V/R, where I is the current, V is the voltage, and R is the resistance. In this case, we have two resistors connected in parallel. Let's assume the voltage of the cell is V.
For the 4-ohm resistor, the current is given as 0.4A. Using Ohm's Law, we can calculate the voltage across the resistor as V1 = I1 * R1 = 0.4A * 4ohms = 1.6V.
For the 10-ohm resistor, the current is given as 0.2A. Using Ohm's Law, we can calculate the voltage across the resistor as V2 = I2 * R2 = 0.2A * 10ohms = 2V.
Since the resistors are in parallel, the voltage across both resistors is the same, so V1 = V2. This means the internal resistance of the cell can be calculated as V = I * r, where r is the internal resistance. Substituting the values, we have 1.6V = 0.4A * r, which gives us r = 1.6V / 0.4A = 4 ohms.
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After scientists have a number of ideas about robot movement in mind, what types of tests do they then perform?
After scientists have a number of ideas about robot movement in mind, they then perform various types of tests to validate their theories and see how the robot actually moves in the real world. Robotics engineers design, build, and program robots, and their work focuses on a few key areas such as mechanics, control theory, electronics, and computer programming. Robotics engineers work in a variety of fields and industries, including manufacturing, aerospace, and healthcare. Before a robot is sent to the market, it must go through rigorous testing to ensure that it functions as intended and meets the safety standards set by regulatory bodies.
To test the robot movement, engineers use computer simulations and physical prototypes. Computer simulations allow engineers to test robot behavior and movement in a virtual environment, while physical prototypes are used to test the robot's movement in the real world. Once the robot has been built, the engineers will test it to see if it moves as intended.
They may also conduct tests to see how the robot performs in different environments or under different conditions.Some of the tests that the engineers might perform to validate their theories include:Simulation tests: Simulation tests are computer-based tests that allow engineers to test the robot's behavior and movement in a virtual environment. Engineers can create different scenarios and see how the robot performs in each scenario. This allows them to fine-tune the robot's programming before it is built.
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A pendulum consists of a mass m hanging at the bottom end of a massless rod of length l, which has a frictionless pivot at its top end. A mass m, moving as shown in the figure with velocity v impacts m and becomes embedded.
The common velocity of masses m and M after the impact is v = mv / sqrt(m (m + M)). A pendulum consists of a mass m hanging at the bottom end of a massless rod of length l, which has a frictionless pivot at its top end. A mass m, moving as shown in the figure with velocity v impacts m and becomes embedded.
The given figure shows the before and after impact of two masses m and M with velocities v and 0, respectively, where mass M is hanging with the help of a rod and performing simple harmonic motion. Therefore, the given system of masses is an example of an inelastic collision. As per the principle of conservation of linear momentum in physics, the momentum of a system is conserved if the net external force acting on it is zero. As the given system of masses has no external force acting on it, its momentum is conserved.
The initial momentum of the system can be calculated as:pi = mv + 0Since mass M is at rest, its initial momentum is zero. Therefore, the total initial momentum of the system ispi = mv. The final momentum of the system can be calculated as:pf = (m + M)V. Here, V is the common velocity of masses m and M after the impact, which can be calculated using the principle of conservation of mechanical energy.
As the given system of masses is an example of an inelastic collision, some energy is lost during the impact due to deformation of the masses. Therefore, the conservation of mechanical energy can be written as:
1/2 mv² = (1/2) (m + M) V²
Solving for V, we get:V² = mv² / (m + M)V = v * sqrt(m / (m + M))
Therefore, the final momentum of the system can be calculated as:pf = (m + M) v * sqrt(m / (m + M)) = v * sqrt(m (m + M))
Therefore, applying the principle of conservation of linear momentum, we have:pi = pfmv = v * sqrt(m (m + M))v = mv / sqrt(m (m + M))
Hence, the common velocity of masses m and M after the impact is v = mv / sqrt(m (m + M)).
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