Energy

1. Energy Kinetic energy Potential energy for z << REarth gravitational electrostatic spring

2. Elastic collisions: p and K conserved Inelastic collisions: p conserved, K not conserved

3. Problem: a bullet of mass mb at speed vb, imbeds and stops within a sand bag ofmass M. What is the maximum height of the sand bag?

4. Taylor expansions (for e << x) Useful to remember Potential gravitational energy for z<<R g constant

5. Potential energy and forces; example: raising an object in grav. field K-work Change in kinetic plus potential energies = Work by EXTERNAL force How to get the potential energy function from a force Will come back to this in C11

6. C6T.5 In a coordinate system where the z axis is vertical, we choose the gravitational potential energy of a 4-kg rock interacting with the earth to be zero when z = -5 m. The formula for the potential energy as a function of z is thus V(z)=mgz+C. What is the (approximate) value of C? • -50 J; • +50 J; • -200 J; • +200 J; • 0 J.

7. C6T.7 Consider a rock interacting gravitationally with the earth. Imagine that we define the interaction potential energy to be zero if the rock is at ground level. A person standing at the bottom of a well throws the rock vertically upward from 20 m below ground level. The rock makes it all the way up to 1 m below ground level before falling back into the well. The total energy of the rock earth system is: • Negative; • Zero; • Positive (in this particular case); • Positive because energy is always positive; • The answer depends on the rock’s mass; • The answer depends on the rock’s initial speed.

8. C7.2 Imagine that we launch a rocket (of mass m) away from the surface of the earth (mass M radius R). Assuming that its engines fire only very briefly at the beginning of its flight, what is the minimum initial speed, vi, that the rocket must have when its engines shut down if it is able to coast away from the earth forever? This speed is called the earth’s escape speed.

9. C7T.3 The general gravitational potential energy formula is always negative for r >0, but the empirical formula is always positive for z > 0. Why are the signs in these expressions different? • The empirical formula is wrong; • The equations refer to different kinds of interactions; • The first equation does not apply to objects that are not point particles; • The equations assume different reference separations.

10. C7T.4 The graph shows the potential energy function of a certain interaction. This interaction is • Always attractive; • Always repulsive; • Attractive for small r, repulsive for large r; • Repulsive for small r, attractive for large r.

11. C7T.6 On a planet twice the mass and twice the diameter of the earth, the value of g at its surface would be what factor times g at the surface of the earth? • 2; • 4; • 8; • ½; • ¼; • 1/8.

12. C7T.8 The potential energy function for a spring is shown in the graph to the right. What is the approximate spring constant for this spring? • 0.05 J/m2; • 5 J/m2; • 50 J/m2; • 100 J/m2; • 200 J/m2.