A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.10 N is applied. A 0.510-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the direction of the initial displacement is positive. Use the exact values you enter to make later calculations.) (a) What is the force constant of the spring? N/m (b) What are the angular frequency w, the frequency, and the period of the motion? @= rad/s Hz S f = T= (c) What is the total energy of the system? J

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.10 N is applied. A 0.510-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the direction of the initial displacement is positive. Use the exact values you enter to make later calculations.) (a) What is the force constant of the spring? N/m (b) What are the angular frequency w, the frequency, and the period of the motion? @= rad/s Hz S f = T= (c) What is the total energy of the system? J

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 spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.10 N is applied. A 0.510-kg particle rests on a frictionless horizontal
surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the
direction of the initial displacement is positive. Use the exact values you enter to make later calculations.)
(a) What is the force constant of the spring?
N/m
(b) What are the angular frequency w, the frequency, and the period of the motion?
W =
rad/s
Hz
f =
T =
S
(c) What is the total energy of the system?
J
(d) What is the amplitude of the motion?
cm
(e) What are the maximum velocity and the maximum acceleration of the particle?
Vmax=
dmax =
m/s
m/s²
(f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s.
cm
a =
(g) Determine the velocity and acceleration of the particle when t = 0.500 s. (Indicate the direction with the sign of your answer.)
V =
m/s
m/s²

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