Conservation of Energy Problem.

Click For Summary
SUMMARY

The conservation of energy problem discusses a cart sliding down a frictionless ramp and colliding with a spring. Initially, the energy equation is established as mgh = 0.5 k D^2, where m is mass, g is gravitational acceleration, h is height, k is spring constant, and D is the initial compression of the spring. When the height is doubled to 2h, the new energy equation becomes mg(2h) = 0.5 k (2D)^2, leading to the conclusion that the spring compresses a distance of 4D.

PREREQUISITES
  • Understanding of gravitational potential energy (mgh)
  • Familiarity with kinetic energy (0.5 k x^2)
  • Knowledge of spring mechanics and Hooke's Law
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems
  • Learn about the behavior of springs under varying loads
  • Explore advanced topics in dynamics involving frictionless surfaces
  • Investigate real-world applications of spring mechanics in engineering
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the principles of energy conservation and spring dynamics.

TwinGemini14
Messages
31
Reaction score
0
A cart, initially at rest, slides down a frictionless ramp onto a horizontal frictionless surface which is a distance h below the original position of the cart. It then collides with the free end of a relaxed horizontal spring, the other end of which is fixed to a wall. As a result the spring compresses a distance D.

Suppose now the initial height is changed to 2h. How far will the spring now compress?

A) sqrt(2)D
B) 2D
C) 4D

------

Initially: mgh = 0.5 k D^2

Suppose: mg(2h) = 0.5 k (2D)^2

So... the spring will now compress 4D. Is this correct?
 
Physics news on Phys.org
Maybe rework your math again?

And remember D is unknown.
 

Similar threads

Question about the conservation of mechanical energy
  • · Replies 7 ·
Replies
7
Views
2K
A block dropping onto a spring system
  • · Replies 58 ·
2
Replies
58
Views
3K
Problem with when to use Force and Energy. What compresses spring/
  • · Replies 3 ·
Replies
3
Views
2K
Find elastic energy in the compressed spring.
  • · Replies 12 ·
Replies
12
Views
3K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
  • · Replies 17 ·
Replies
17
Views
2K
Spring Problem Involving Variables and Constants Only
  • · Replies 3 ·
Replies
3
Views
2K
A cart collides with a bumper -- Find the final displacements, etc.
  • · Replies 15 ·
Replies
15
Views
2K
A rocket on a spring, related to potential/kinetic energy
  • · Replies 3 ·
Replies
3
Views
2K
Conservation of Energy of cart Problem
  • · Replies 5 ·
Replies
5
Views
5K
Why doesn't this solution work? (Springs and Conservation of Energy)
  • · Replies 2 ·
Replies
2
Views
2K