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Potential Energy

Potential energy lets us do work in the present to change things in the future. If energy is currency, then potential energy is money in the bank.

Problem Solving

A grandfather clock works by a pendulum system and keeps time because the pendulum has a constant frequency. The grandfather clock in my room has stopped, but I'm too lazy to get out of bed to start the pendulum oscillating again. Hence I throw a sticky piece of gum at the pendulum to get it moving again. My piece of gum has a mass of 10 g, hits the pendulum inelastically with a speed of 10 m/s, and sticks there. Admittedly disgusting. But, more importantly, if the pendulum has a mass of 90 g, how high does the pendulum on my grandfather clock go in meters?

Details and assumptions

  • The acceleration due to gravity is \(9.8~m/s^2\).
  • Treat the grandfather clock as a simple pendulum.

An object of mass \(m=9\text{ kg}\) is released from rest at point \(A,\) and slides down a long, frictionless, \(h=60\text{ m}\) high slide. Then it enters the horizontal surface from point \(B\) to \(C,\) which is not frictionless, and comes to a complete stop at point \(C.\) If the coefficient of kinetic friction between the object and the surface is \(\mu=0.1,\) what is the horizontal distance \(x\) between points \(B\) and \(C?\)

The gravitational acceleration is \(g=10\text{ m/s}^2.\)

An object of mass \(4\text{ kg}\) initially at rest falls freely towards a huge spring that is \(100\text{ m}\) below. If the spring constant is \(k=16\text{ N/m},\) what is the maximum change in the spring's length?

Air resistance is negligible and gravitational acceleration is \(g=10\text{ m/s}^2.\)

While an object of mass \(10\text{ kg}\) drops from the edge of a \(60\)-meter-high cliff, it experiences air resistance, whose strength during the descent is constantly \(15\text{ N}.\) What is the square of the velocity with which the object hits the ground?

A meteor of mass \(m=800\text{ kg}\) enters the earth's atmosphere with a velocity of \(500\text{ m/s},\) and falls vertically toward the ground. The meteor burns while falling, and its mass decreases at a rate of \(5\text{ kg/s}.\) If the meteor falls with a constant velocity, how much gravitational potential energy will it lose during \(16\) seconds?

Note

  • The height of the meteor when it enters the atmosphere is \(1000\text{ km},\)
  • The gravitational acceleration is \(g=10\text{ m/s}^2.\)
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