Perfect Elastic Collision of a Mass Attached to a Spring

Perfect Elastic Collision of a Mass Attached to a Spring#

A block of mass m1 slides across a frictionless surface with speed v1 and collides perfectly elastically with a block m2 (initially at rest). Block m2 is attached to a spring with spring constant k and equilibrium length x0. Assume m2>m1.

A block of mass m one slides across a frictionless surface with speed v one and collides perfectly elastically with a block m two attached to a spring with spring constant k and equilibrium length x naught.

Part 1#

What is the amplitude of the resulting simple harmonic motion? Answer using the variables m1,m2,k,x0 and/or v1.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

Variable

Use

m1

m1

m2

m2

x0

x0

k

k

v1

v1

Answer Section#

Enter answer here…

Part 2#

What is the period of the resulting simple harmonic motion? Answer using the variables m1,m2,k,x0 and/or v1.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

Variable

Use

m1

m1

m2

m2

x0

x0

k

k

v1

v1

Answer Section#

Enter answer here…

Part 3#

What is the position of m2 as a function of time? Note that the +x direction is defined as to the right in the diagram. Assume t=0 at the time of collision. Answer using the variables t,A and/or ω.

Note that it may not be necessary to use every variable and that the correct answer will simplify all trigonometric functions (simplifying your answer is not required). Use the following table as a reference for each variable:

Variable

Use

t

t

A

A

ω

w

Answer Section#

Enter answer here…

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.