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EXERCISE What if, in the Example, m₁ is initially moving at 3.8 m/s while m2 is initially at rest? Hint For part (a), apply conservation of momentum to find the velocity of the combined masses when the spring is compressed. In this case the initial momentum is the initial velocity of m₁ times its mass, and the final momentum is the sum of the two masses times v. Then find the initial kinetic energy and the kinetic energy of the combined masses, and take the difference. This energy has gone into compressing the spring, so set it equal to the expression for the spring potential energy to find Ax, the maximum spring compression. For part (b), again apply conservation of momentum, and conservation of energy, since the collision is perfectly elastic. (a) Find the maximum spring compression (in m) in this case. m Click the hint button again to remove this hint. (b) What will be the individual velocities of the two masses (V₁ and 2) after the spring extended fully again? (That is, when the two masses separate from each other after the collision is complete. Enter the magnitudes in m/s.) V1 = m/s to the left = m/s to the right A Two-Body Collision with a Spring A block of mass m₁ = 1.50 kg initially moving to the right with a speed of 5.00 m/s on a frictionless, horizontal track collides with a light spring attached to a second block of mass m₂ initially moving to the left with a speed of 2.50 m/s as shown in figure (a). The spring constant is 550 N/m. (Assume the positive direction points to the right.) Before a moving block collides with another moving block with a spring attached. a m k V2i m2 At one instant during the collision. k m1 m2 wwwwww b = 6.50 kg

EXERCISE What if, in the Example, m₁ is initially moving at 3.8 m/s while m2 is initially at rest? Hint For part (a), apply conservation of momentum to find the velocity of the combined masses when the spring is compressed. In this case the initial momentum is the initial velocity of m₁ times its mass, and the final momentum is the sum of the two masses times v. Then find the initial kinetic energy and the kinetic energy of the combined masses, and take the difference. This energy has gone into compressing the spring, so set it equal to the expression for the spring potential energy to find Ax, the maximum spring compression. For part (b), again apply conservation of momentum, and conservation of energy, since the collision is perfectly elastic. (a) Find the maximum spring compression (in m) in this case. m Click the hint button again to remove this hint. (b) What will be the individual velocities of the two masses (V₁ and 2) after the spring extended fully again? (That is, when the two masses separate from each other after the collision is complete. Enter the magnitudes in m/s.) V1 = m/s to the left = m/s to the right A Two-Body Collision with a Spring A block of mass m₁ = 1.50 kg initially moving to the right with a speed of 5.00 m/s on a frictionless, horizontal track collides with a light spring attached to a second block of mass m₂ initially moving to the left with a speed of 2.50 m/s as shown in figure (a). The spring constant is 550 N/m. (Assume the positive direction points to the right.) Before a moving block collides with another moving block with a spring attached. a m k V2i m2 At one instant during the collision. k m1 m2 wwwwww b = 6.50 kg

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter7: Conservation Of Energy
Section: Chapter Questions
Problem 73P: A block of mass m1 = 20.0 kg is connected to a block of mass m2 = 30.0 kg by a massless string that...
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EXERCISE What if, in the Example, m₁ is initially moving at 3.8 m/s while m2 is initially at rest? Hint For part (a), apply conservation of momentum to find the velocity of the combined masses when the spring is compressed. In this case the initial momentum is the initial velocity of m₁ times its mass, and the final momentum is the sum of the two masses times v. Then find the initial kinetic energy and the kinetic energy of the combined masses, and take the difference. This energy has gone into compressing the spring, so set it equal to the expression for the spring potential energy to find Ax, the maximum spring compression. For part (b), again apply conservation of momentum, and conservation of energy, since the collision is perfectly elastic. (a) Find the maximum spring compression (in m) in this case. m Click the hint button again to remove this hint. (b) What will be the individual velocities of the two masses (V₁ and 2) after the spring extended fully again? (That is, when the two masses separate from each other after the collision is complete. Enter the magnitudes in m/s.) V1 = m/s to the left = m/s to the right
Transcribed Image Text:EXERCISE What if, in the Example, m₁ is initially moving at 3.8 m/s while m2 is initially at rest? Hint For part (a), apply conservation of momentum to find the velocity of the combined masses when the spring is compressed. In this case the initial momentum is the initial velocity of m₁ times its mass, and the final momentum is the sum of the two masses times v. Then find the initial kinetic energy and the kinetic energy of the combined masses, and take the difference. This energy has gone into compressing the spring, so set it equal to the expression for the spring potential energy to find Ax, the maximum spring compression. For part (b), again apply conservation of momentum, and conservation of energy, since the collision is perfectly elastic. (a) Find the maximum spring compression (in m) in this case. m Click the hint button again to remove this hint. (b) What will be the individual velocities of the two masses (V₁ and 2) after the spring extended fully again? (That is, when the two masses separate from each other after the collision is complete. Enter the magnitudes in m/s.) V1 = m/s to the left = m/s to the right
A Two-Body Collision with a Spring A block of mass m₁ = 1.50 kg initially moving to the right with a speed of 5.00 m/s on a frictionless, horizontal track collides with a light spring attached to a second block of mass m₂ initially moving to the left with a speed of 2.50 m/s as shown in figure (a). The spring constant is 550 N/m. (Assume the positive direction points to the right.) Before a moving block collides with another moving block with a spring attached. a m k V2i m2 At one instant during the collision. k m1 m2 wwwwww b = 6.50 kg
Transcribed Image Text:A Two-Body Collision with a Spring A block of mass m₁ = 1.50 kg initially moving to the right with a speed of 5.00 m/s on a frictionless, horizontal track collides with a light spring attached to a second block of mass m₂ initially moving to the left with a speed of 2.50 m/s as shown in figure (a). The spring constant is 550 N/m. (Assume the positive direction points to the right.) Before a moving block collides with another moving block with a spring attached. a m k V2i m2 At one instant during the collision. k m1 m2 wwwwww b = 6.50 kg
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