Finding the Compression of a Spring Using the Work-Energy Theorem

[student34]

Homework Statement

A 6.0kg box moving at 3.0m/s on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Use the work-energy theorem to find the maximum compression in the spring.

Homework Equations

W = K2 - K1

W = (1/2)*m*v^2 - (1/2)*m*vo^2

W = - (1/2)*k*x^2

The Attempt at a Solution

- (1/2)*k*x^2 = 0 - (1/2)*m*vo^2, where k = 75000N/m

x = ((m*v^2)/k)^(1/2) = ((6.0kg*(3m/s)^2)/75000N/m)^(1/2)

x = 0.027m

But the answer in the book is x = 0.085m. I just can't see what I am doing wrong unless my textbook is wrong.

 

[Averki]

Recheck your value for k.

 

[student34]

Recheck your value for k.

Oh my god, thanks!

 

[semaj nayr]

Homework Statement

A 6.0kg box moving at 3.0m/s on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Use the work-energy theorem to find the maximum compression in the spring.

Homework Equations

W = K2 - K1

W = (1/2)*m*v^2 - (1/2)*m*vo^2

W = - (1/2)*k*x^2

The Attempt at a Solution

- (1/2)*k*x^2 = 0 - (1/2)*m*vo^2, where k = 75000N/m

x = ((m*v^2)/k)^(1/2) = ((6.0kg*(3m/s)^2)/75000N/m)^(1/2)

x = 0.027m

But the answer in the book is x = 0.085m. I just can't see what I am doing wrong unless my textbook is wrong.

It's your conversion of N/cm to N/m sir. It is only 7,500 instead of 75,000. But thanks so much for this

 

[PeroK]

It's your conversion of N/cm to N/m sir. It is only 7,500 instead of 75,000. But thanks so much for this

Note that this thread is nine years old.