Work and Energy

Question 1

What is the integral of F dx equal to?

Answer 1

The integral of dT, which is equal to the change in kinetic energy and therefore the work done W.

Question 2

What is the infinitesimal version of the work done dW?

Answer 2

dW = F dx = dT, where T is the kinetic energy.

Question 3

What is the general equation for kinetic energy T in 3D?

Answer 3

T = 1/2 * m(vx^2+vy^2+vz^2) = 1/2m*v- . v-, where . is the dot product and v- is the vector of v.

Question 4

What is the 3D version of dW?

Answer 4

dW = F.dr = dT

Question 5

What is a conservative force field?

Answer 5

A force field in which the work done is independent of the path.

Question 6

Why is the potential negative?

Answer 6

To ensure the work done is positive when moving from a high to low potential.

Question 7

What is the kinetic energy added to the potential energy U equal to?

Answer 7

A constant, E. This is the total energy.

Question 8

How do you derive a force from a potential?

Answer 8

F = -dU/dx = -dU/dx i -dU/dy j -dU/dz k = -∇U

Question 9

What is the equation for gravitational potential energy U(r)?

Answer 9

U(r) = -GMm/r

Question 10

How do you work out the escape velocity of the Earth?

Answer 10

Set kinetic energy equal to gravitational potential energy.

Question 11

What is the equation for Power?

Answer 11

P = dW/dt = F.dr/dt = F.v