Classical Mechanics

Potential Energy

Potential Energy - 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/s29.8~m/s^2.
  • Treat the grandfather clock as a simple pendulum.

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

The gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

An object of mass 4 kg4\text{ kg} initially at rest falls freely towards a huge spring that is 100 m100\text{ m} below. If the spring constant is k=16 N/m,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 m/s2.g=10\text{ m/s}^2.

While an object of mass 10 kg10\text{ kg} drops from the edge of a 6060-meter-high cliff, it experiences air resistance, whose strength during the descent is constantly 15 N.15\text{ N}. What is the square of the velocity with which the object hits the ground?

A meteor of mass m=800 kgm=800\text{ kg} enters the earth's atmosphere with a velocity of 500 m/s,500\text{ m/s}, and falls vertically toward the ground. The meteor burns while falling, and its mass decreases at a rate of 5 kg/s.5\text{ kg/s}.

If the meteor falls with a constant velocity, how much gravitational potential energy will it lose in 1616 seconds?

Note

  • The height of the meteor when it enters the atmosphere is 1000 km,1000\text{ km},
  • The gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.
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