Your roommate peeks over your shoulder while you are reading a physics text* and notices the following sentence: "In free-fall the acceleration is always g and always straight downward regardless of the motion." Your roommate finds this peculiar and raises three objections:

1. If I drop a balloon or a feather, it doesn't fall nearly as fast as a brick.
2. Not everything falls straight down; if I throw a ball it can go sideways.
3. If I hold a wooden ball in one hand and a steel ball in the other, I can tell that the steel ball is being pulled down much more strongly than the wooden one. It will probably fall faster.

* Physics, by E. Hecht (Brooks Cole Publishers, 1994)

A ball is launched up a ramp by a spring as shown in the figure at the right. At the time when the clock starts, the ball is near the bottom of the ramp and rolling up the ramp as shown. It goes to the top and then rolls back down. For the graphs shown below, the horizontal axis represents the time. The vertical axis is unspecified.

An old Yiddish joke is told about a farmer in Chelm, a town famous for the lack of wisdom of its inhabitants. One day the farmer was going to the mill to have a bag of wheat ground into flour. He was riding to the mill on his donkey, with the sack of wheat thrown over the donkey's back behind him. On his way, he met a friend. His friend chastised him. "Look at you! You must weigh 200 pounds and that sack of flour must weigh 100. That's a very small donkey! Together, you're too much weight for him to carry!" On his way to the mill the farmer thought about what his friend had said. On his way home, he passed his friend again, confident that this time the friend would be satisfied. The farmer still rode the donkey, but this time he carried the 100 pound bag of flour on his own shoulder!

Our common sense and intuitions seem to suggest that it doesn't matter how you arrange things, they'll way the same. Let's be certain that the Newtonian framework we are developing yields our intuitive result. Analyze the problem by considering the following simplified picture: two blocks resting on a scale. One block weighs 10 N, the other 25 N. In case 1 the blocks are arranged on the scale as shown in the figure on the left. In case 2 the blocks are arranged as shown on the right. Each system has come to rest. Analyze the forces on the blocks and on the scale in the two cases by isolating the objects -- each block and the scale -- and using Newton's laws, show that according to the principles of Newton's laws, the total force exerted on the scale by both blocks together must be the same in both cases. (Note: It's not enough to say: "They have to be the same." That's just restating your intuition. We need to see that reasoning using only the principles of our Newtonian framework leads to the same conclusion.)

The figure at the right shows a multiple-exposure photograph of a ball rolling up an inclined plane. (The ball is rolling in the dark, the camera lens is held open, and a brief flash occurs every 3/4 sec four times.) The left-most ball corresponds to an instant just after the ball was released. The right-most ball is at the highest point the ball reaches.

1. Copy this picture on your paper and, at each ball, draw an arrow to indicate the velocity of the ball at the instant when it was at that point in space. Explain what is happening ("tell the story" of the picture).

2. For the instant of time when the ball is at the second position shown from the left, draw a free-body diagram for the ball and indicate all forces acting on it.

3. If your force diagram doesn't include an arrow pointing up the ramp, explain why the ball keeps rolling up the ramp.

4. If the mass of the ball is m, what is its acceleration?

5. If the angle q is equal to 30^o, how long is the distance s?

George left the lights in his truck on while in a truck stop in Kansas and his battery went dead. Fortunately, his friend Al was there. Unfortunately, Al was driving his Geo Metro. Fortunately, the road was very flat. George was able to convince Al to give his truck a long slow push to get it up to 20 miles/hour. At this speed, George can let in the truck's clutch and the truck's engine should start up.

1. Al begins to push the truck. It takes him 5 minutes to get the truck up to a speed of 20 miles/hour. During the time that Al's Geo is pushing the truck, draw separate free body diagrams for the Geo and for the truck. Order all the horizontal forces by magnitude from largest to smallest. If any are equal, state that explicitly. Explain your reasoning.

2. If the truck was accelerating uniformly over the 5 minutes, how far did Al have to push the truck before George could let in the clutch?

3. Suppose the mass of the truck is 4000 kg, the mass of the car is 800 kg, and the coefficient of friction between the vehicles and the road is 0.1. At one instant when they were trying to get the truck moving, the car was pushing the truck and exerting a force of 1000 N, but neither vehicle moved. What was the frictional force between the truck and the road? Explain your reasoning.

A popgun is angled so that it shoots a small dense ball through the air as shown in the figure. a. Sketch the path that the ball will follow on the figure.

For the graphs shown at the right, the horizontal axis represents the time. The vertical axis is unspecified. For each of the following quantities, select the letter of the graph that could provide a correct graph of the quantity for the ball in the situation shown (if the vertical axis were assigned the proper units). Use the x and y coordinates shown in the picture. If none of the graphs could work write N. The time graphs begin just after the ball leaves the gun. y coordinate x component of the velocity y component of the net force y component of the velocity x coordinate y component of the acceleration x component of the net force

In class we did a demonstration in which two objects of different masses were dropped, one straight down, and the other shot off to the side by a spring. Both objects seemed to hit the ground at about the same time. Explain why this happens in terms of the physics we have learned. Does it matter how fast we shoot the one launched sideways?