Spring-Block Work Done

  • #1
Moved from technical forum, so no template
Hi - I'm looking for some help with the solution of this problem

"A 1 kg block situated on a rough incline is connected to a spring with spring constant 100 Nm-1 as shown in Figure. The block is released from rest with the spring in the unstretched position. The block moves 10 cm down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has negligible mass and the pulley is friction less."
28765499061_81e18a0887_o.png


The solution given is :
28841587685_728ffc9ff8_o.png


I tried to solve the problem based on the final equilibrium state - without calculating the work done. The equations I end up with are:

Block: mg sin θ = µ mg cos θ + T
Spring end: T = kx

Leading to : mg (sin θ - µ cos θ) = kx

This is off by factor of 2 compared to the solution above.

What's the right approach to solve the problem?
 

Attachments

Answers and Replies

  • #2
stockzahn
Homework Helper
Gold Member
498
136
Block: mg sin θ = µ mg cos θ + T
Unfortunately, that's a wrong assumption in this scenario. The friction force is a reaction force. Imagine ##\mu## to have exactely a value, so that the block stops at a position ##x## for which ##kx=mg\;sin \theta##. Then the two forces are in equilibrium, the block does not move and no friction force is acting on it. Therefore your approach in this case is not applicable.
 
  • #3
Unfortunately, that's a wrong assumption in this scenario. The friction force is a reaction force. Imagine ##\mu## to have exactely a value, so that the block stops at a position ##x## for which ##kx=mg\;sin \theta##. Then the two forces are in equilibrium, the block does not move and no friction force is acting on it. Therefore your approach in this case is not applicable.
Understood. Thanks!
 

Related Threads on Spring-Block Work Done

Replies
1
Views
15K
Replies
4
Views
5K
Replies
4
Views
4K
Replies
5
Views
1K
Replies
3
Views
2K
Replies
4
Views
7K
Replies
3
Views
2K
  • Last Post
Replies
11
Views
871
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
1K
Top