Forces, Uniform Circular Motion, and Gravity Review

1. Forces, Uniform Circular Motion, and Gravity Review October 7

2. m1 47 60 m1 m2 0 m2 a1 F a2 = 2a1 F a3 F 0 A force F acts on mass m1giving acceleration a1. The same force acts on a different mass m2 giving acceleration a2= 2a1. What is the acceleration if the same force pushes on both blocks? • 4/3 a1 • 3/2 a1 • 1/2 a1 • 3/4 a1 • 2/3 a1

3. 99 Astronauts can not weigh themselves on a conventional scale (no normal force is produced). Discuss with your neighbor ways of measuring the mass of an astronaut while in space. • . • .

4. 47 60 0 0 When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that? • this slows your initial velocity which is already upward • you don’t go up, you’re too heavy • you’re not really pulling down -- it just seems that way • the rope actually pulls you up • you are pulling the ceiling down

5. m1 m1 A B m2 m2 47 F 60 F 0 0 If you push with force F on either the heavy box (m1) or the light box (m2), in which of the two cases below is the contact force between the two boxes larger? • Case A • Case B • Same in both cases

6. a 47 60 T3 T2 T1 3m 2m m 0 0 Three blocks of mass 3m, 2m, and m are connected by strings and pulled with constant acceleration a. What is the relationship between the tension in each of the strings? • T1 > T2 > T3 • T1 < T2 < T3 • T1 = T2 = T3 • all tensions are zero • tensions are random

7. 47 Normal 60 0 Net Force Weight 0 A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? • The component of the gravity force parallel to the plane increased • coeff. of static friction decreased • normal force exerted by the board decreased • both #1 and #3 • all of #1, #2 and #3

8. 60 4 5 1 3 2 47 0 0 A ping pong ball is shot into a circular tube which is lying flat (horizontal) on a tabletop. When the ping pong ball leaves the track, which path will it follow? • 1 • 2 • 3 • 4 • 5

9. 3 5 2 1 4 47 60 0 0 A rider in a “barrel of fun” finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her? • 1 • 2 • 3 • 4 • 5

10. top v 47 60 R 0 0 You swing a ball at the end of string in a vertical circle. Since the ball is in circular motion there has to be a centripetal force. At the top of the ball’s path, what is Fc equal to? • Fc =FT - mg • Fc =FT + FN - mg • Fc =FT + mg • Fc =FT • Fc =mg

11. 2d 2m 5 Earth 4 d 3 2 1 m 47 60 0 0 A planet of mass m is a distance d from Earth. Another planet of mass 2m is a distance 2d from Earth. Which force vector best represents the direction of the total gravitation force on Earth? • 1 • 2 • 3 • 4 • 5

12. Answers • 5 – 2/3 a since m1+m2=3/2m1 • Apply known force and measure acceleration (this assumes inertial mass = gravitational mass, which is now experimental fact) • 4 • 1 – Case A – Fcontact must push a larger mass for same acceleration • 1 • 4 – 1 and 3 • 2 • 1 – mg, friction, normal • 3 – if velocity is just right so mv^2/R=mg, then tension=0 and momentarily in freefall • 2 – gravity is directly proportional to m and inversely proportional to R^2, so bigger planet farther away in this case has ½ the gravitational force, so does not add an equal component to total force as the smaller, closer planet