physics conservative energy problem?

Question

1)

The net force acting on a particle is conservative and increases the kinetic energy by 300J. What is the change in:
a. potential energy
b. total energy

I was thinking that the potential energy wouldn't change because the kinetic energy is dependant on the velocity.

2)

Analyze the motion of a simple swinging pendulum in terms of energy
(a) ignoring friction
(b) taking friction into account
Explain why the grandfather clock must be wound up.

I was thinking the net work would be zero in a grandfather clock if the friction was zero. I was also thinking that with friction the kinetic energy would be depleted by the nonconservative force of friction and the net force would eventually become zero.

Thanks!

Answer 1

1)
The conservation of energy principle tells us that energy is neither created nor destroyed, but it changes form. If you apply a conservative force, this principle will hold. That is, the force does not take energy away from the system. If kinetic energy increases, there is a corresponding decrease in potential energy. The total energy of the particle doesn't change, but the 300J is converted from potential to kinetic. You are correct that the kinetic energy is velocity related, but in this case, the velocity will increase.

2)
If you ignore friction in the pendulum, it will keep swinging until you apply a force to stop it. At the height of the swing, all of the energy is potential (since it is at rest and gravity is acting downwards on it). As it begins to swing, potential energy decreases as the velocity increases. At the bottom of the swing, it is all kinetic until it loses energy to gravity and the potential energy increases until it hits the top of the swing again (to the same height as it was released from). This keeps going.

If you take friction into account, part of the energy is converted to heat from the friction. As the pendulum swings, it loses some energy and it will not reach the same heigh in the swing as it did previously. Each swing will go to a lower height as it did before until eventually all the energy is lost to heat. You wind the clock up to add energy that was lost to heat.

Hope this helps.