Sphere rolls down and compresses spring

  • Thread starter Thread starter scruffles
  • Start date Start date
  • Tags Tags
    Sphere Spring
Click For Summary
SUMMARY

A solid sphere rolls down an incline and compresses a spring, with no energy loss due to friction. The problem requires finding an expression for the spring's compression in terms of the sphere's mass (m), radius (R), vertical displacement (h), and spring constant (k). The relevant equations include potential energy (V = mgh), spring potential energy (V = 1/2 kx^2), and kinetic energy (K = 1/2 mv^2 + Iω^2). The conservation of energy principle is essential for solving this problem.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with potential and kinetic energy equations
  • Knowledge of rotational dynamics and moment of inertia
  • Basic calculus for deriving expressions
NEXT STEPS
  • Study the derivation of energy conservation in rolling motion
  • Learn about the moment of inertia for solid spheres
  • Explore the relationship between linear and angular velocity
  • Investigate the effects of friction in rolling motion scenarios
USEFUL FOR

Students in physics, particularly those studying mechanics, as well as educators and anyone interested in understanding energy conservation in rolling objects.

scruffles
Messages
8
Reaction score
0

Homework Statement


torque1.png

image host

A solid sphere rolls without slipping down an incline and compresses a spring. The figure above shows the system with the spring compressed to its turning point (at maximum compression, where the sphere’s velocity is zero.) Assume that no energy is lost due to non-conservative forces such as friction as the sphere rolls down the incline and compresses the spring. The distance h is the vertical displacement of the sphere’s center of mass, m is its mass, R is its radius, and k is the spring constant.
In terms of the variables stated, find an expression for the amount the spring is compressed.

Homework Equations


V= 1/2kx^2
V= mgh
K=1/2mv^2 + Iomega^2

The Attempt at a Solution


I honestly am stuck here. Any tips or ideas would be great! Thanks in advance!
 
Physics news on Phys.org
Apply conservation of energy. What are the values of all kinds of energy on the top of the hill? And what are at the bottom, when the spring is compressed, and the velocity is zero?


ehild
 
Last edited:

Similar threads

Distribution of Energy when work is done on a system of 2 masses connected by a spring
  • · Replies 17 ·
Replies
17
Views
2K
A cart collides with a bumper -- Find the final displacements, etc.
  • · Replies 15 ·
Replies
15
Views
2K
Conservation: Mass Dropped onto a Spring, Find the Compression
  • · Replies 9 ·
Replies
9
Views
2K
Question about springs and rotational/translational energy
  • · Replies 4 ·
Replies
4
Views
2K
Period and Velocity of Oscillating Sphere Attached to Spring
  • · Replies 10 ·
Replies
10
Views
2K
A block of mass m is dropped onto the top of a vertical spring....
  • · Replies 8 ·
Replies
8
Views
6K
Elastic potential energy (spring) problem
  • · Replies 3 ·
Replies
3
Views
2K
An error made in a kinematics question about a spring launcher?
  • · Replies 16 ·
Replies
16
Views
2K
Solving a Spring-Mass-Box System:Energy Conservation
  • · Replies 1 ·
Replies
1
Views
2K
Homework help: Work and Energy: Spring
  • · Replies 3 ·
Replies
3
Views
1K