A block of mass m1 travels at a speed of v0 on a frictionless horizontal surface

Question

A block of mass m1 travels at a speed of v0 on a frictionless horizontal surface when it comes upon a second block of mass m2 which is initially motionless. Block m2 has a massless spring with spring constant k in front of it.

a. Explain why the linear momentum of the system of two blocks and spring is or is not conserved during the collision.

b. Explain why the mechanical energy of the system of two blocks and spring is or is not conserved during the collision.

c. Consider a time when the spring is compressed a distance x from its equilibrium length. Write the equations for the conservation of momentum and conservation of energy at this instant.

d. Now consider the instant when the spring is compressed as far as it will ever be compressed, a displacement L from its equilibrium length. What are the velocities of the two masses at this instant?

e. What is the spring’s maximum compression L in terms of m1, m2, k, and v0, or a subset of these quantities?

A block of mass m, travels at a speed of v on a frictionless horizontal surface when it comes upon a second block of mass m2 which is initially motionless. Block m, has a massless spring with spring constant k in front of it. a. Explain why the linear momentum of the system of two blocks and spring is or is b. Explain why the mechanical energy of the system of two blocks and spring is or is c. Consider a time when the spring is compressed a distance x from its equilibrium not conserved during the collision. not conserved during the collision. length. Write the equations for the conservation of momentum and conservation of energy at this instant. d. Now consider the instant when the spring is compressed as far as it will ever be compressed, a displacement L from its equilibrium length. What are the velocities of the two masses at this instant? subset of these quantities? spring, what is the final velocity of block m? e. What is the spring's maximum compression L in terms of m,, m2, k, and vo, or a f. In the end, when block m, has been pushed away and is no longer touching the

Explanation / Answer

a)

the linear momentum of the system is conserved . since there is no external force acting on the system . all the forces are internal

b)

the mechanical energy of the system is also conserved , since there is no external force and hence no loss of energy .

c)

m1 vo = m1 v1 + m2 v2

using conservation of energy

(0.5) m1 v2o = (0.5)m1 v21 + (0.5) m2 v22 + (0.5) k x2

d)

when the spring is fully compressed , both the masses move at same speed "V"

using conservation of momentum

m1 vo = (m1 + m2) v

using conservation of energy

(0.5) m1 v2o = (0.5)(m1 +   m2 ) v2 + (0.5) k L2

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