Chapter 7 Work and Energy

6-3 Gravity Near the Earth’s Surface; Geophysical Applications Example 6-5: Effect of Earth’s rotation on g. Assuming the Earth is a perfect sphere, determine how the Earth’s rotation affects the value of g at the equator compared to its value at the poles.

6-4 Satellites and “Weightlessness” Satellites are routinely put into orbit around the Earth. The tangential speed must be high enough so that the satellite does not return to Earth, but not so high that it escapes Earth’s gravity altogether.

6-4 Satellites and “Weightlessness” The satellite is kept in orbit by its speed—it is continually falling, but the Earth curves from underneath it.

Newton’s Law of Universal Gravitation and satellites Satellites and planets are kept in orbit by gravitational force r r We will treat the orbits as circular, so the acceleration is towards the center of the circle

6-4 Satellites and “Weightlessness” Objects in orbit are said to experience weightlessness. They do have a gravitational force acting on them, though! The satellite and all its contents are in free fall, so there is no normal force. This is what leads to the experience of weightlessness.

Apparent Weight Scale in an elevator: The apparent weight has a magnitude of F N and points in the direction opposite the normal force. FNFN

6-4 Satellites and “Weightlessness” More properly, this effect is called apparent weightlessness, because the gravitational force still exists. It can be experienced on Earth as well, but only briefly:

Question A boy pulls a sled across the snow 10 m. The work done on the sled by the normal force is A) Positive B) Negative C) Zero Normal

Question A boy pulls a sled across a level field of snow. The work done on the sled by gravity is A) Positive B) Negative C) Zero Gravity

Question A boy pulls a sled across the snow 10 m. The work done on the sled by the Boy is A) Positive B) Negative C) Zero Force Boy

A pendulum bob is swinging back and forth in an arc in the plane of the page as seen below. The Tension force is 20 N, and the arc length is 5 m. The Work done by the Tension force in one quarter swing (up or down) is A) Positive B) Negative C) Zero D) Depends on the direction of the swing T Question

Alice lifts a 1 kg box 2 meters off the ground at a constant speed where gravity = 10m/s 2 Work done by gravity is: A) +20 Nm B) -20 Nm C) 0 D) -5 Nm E) +5 Nm 2 m

7-1 Work Done by a Constant Force Work done on a crate. A person pulls a 50-kg crate 40 m along a horizontal floor by a constant force F P = 100 N, which acts at a 37° angle as shown. The floor is exerts and exerts a friction force F fr =50N. Determine (a) the work done by each force acting on the crate, and (b) the net work done on the crate.

9.(II) A box of mass 6.0 kg is accelerated from rest by a force across a floor at a rate of 2m/s 2 for 7.0 s. Find the net work done on the box. Problem 9

Problem (II) (a) What magnitude force is required to give a helicopter of mass M an acceleration of 0.10 g upward? (b) What work is done by this force as the helicopter moves a distance h upward?