A toy car of mass m is pushed against a spring, compressing it a distance d from its natural rest length. The spring exerts a force F(x) = −(kx + ßx³)îx, where x is the displacement from its equilibrium position at the origin. The car is then released from rest and slides on a table with coefficient of friction u. (i) What is the car's speed when it reaches the origin? (ii) If the car detaches from the spring when it reaches the origin, derive an equation that could be solved to find the location of the car when it comes to rest (do not solve).

A toy car of mass m is pushed against a spring, compressing it a distance d from its natural rest length. The spring exerts a force F(x) = −(kx + ßx³)îx, where x is the displacement from its equilibrium position at the origin. The car is then released from rest and slides on a table with coefficient of friction u. (i) What is the car's speed when it reaches the origin? (ii) If the car detaches from the spring when it reaches the origin, derive an equation that could be solved to find the location of the car when it comes to rest (do not solve).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

A toy car of mass m is pushed against a spring, compressing it a distance d
from its natural rest length. The spring exerts a force F(x) = −(kx + ßx5)ix, where x
is the displacement from its equilibrium position at the origin. The car is then released
from rest and slides on a table with coefficient of friction µ. (i) What is the car's speed
when it reaches the origin? (ii) If the car detaches from the spring when it reaches the
origin, derive an equation that could be solved to find the location of the car when it
comes to rest (do not solve).
Law
Application
Foooo
d
m
0
X

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