Despite your rigorous academic
schedule, you always find time for intramural sports. This semester, you’ve
signed up to play volleyball. Several teams have sought you out because of your
incredible spike. In that spike, you leap two feet into the air as the ball
comes toward you over the net. You then take your fist and hammer the ball
forward and downward so that it strikes the floor inside your opponent’s area
at about 100 mph. The ball rebounds so fast and so far that no one on the
opposing side can touch it. You’re easily worth 10 points a game. After some
indecision, you pick a team and are soon out on the court for your first game.
Only moments into that game, it’s time for one of your trademark spikes!
Important Note: While air normally affects the
volleyball’s flight in ways that are critical to the game, please ignore air
resistance and other air effects in the following questions.
1. The ball is coming toward you over the net and is presently at the top of its arc—the highest point in its flight from one side of the court to the other. You haven’t touched the ball yet. What are the directions of (a) the ball’s velocity and (b) the ball’s acceleration, and (c) is there a force acting on the ball to keep it moving forward in the horizontal direction? If there is a force, in which direction does it act and what type of force is it?
Answer: (a) The ball's velocity is horizontal and forward (toward you), (b) its acceleration is directly downward, and (c) there is no force pushing it in the forward horizontal direction.
Why: At the top of its arc, the ball has stopped rising and is about to start descending, so it has no vertical component to its velocity. However, it is still heading toward you, so it does have a forward horizontal component to its velocity. Overall, its velocity points directly forward and horizontal. Its acceleration is due entirely to the downward force of gravity and is in that same downward direction. And the ball is moving forward only because of its inertia. There is no force pushing the ball forward horizontally.
2. It’s time for the spike. You swing your arm around and hit the ball hard. You’re pushing it mostly forward. The amount of force you exert on the ball is far greater than the ball’s weight. Explain how you can push on the ball with a force greater than the ball’s weight, even though the ball has nothing else touching it.
Answer: You are making the ball accelerate forward rapidly and this requires that you push on it with an enormous forward force.
Why: The force that you exert on the ball has nothing to do with gravity or the ball's weight. It's simply a matter of mass, acceleration, and Newton's second law. If you want the ball to accelerate forward quickly, you must push it forward hard. There is no limit to your forward force, although your hand and the ball can't tolerate forces that are too great.
3. Before you touch the ball, it’s coming toward you. As you hit it, it first comes almost to a stop and then picks up speed in the opposite direction. It finally leaves your hand traveling away from you and moving faster than before you touched it. This means that the ball’s kinetic energy first decreased nearly to zero and then increased to an enormous amount. Use the concept of work to show how the impact of your hand first took energy out of the ball and then added energy to the ball. (Important Note: the volleyball itself isn’t rigid. When you’re touching it, the overall ball doesn’t necessarily move in the direction of your hand. Sometimes your hand and the ball even move in opposite directions, at least for a little while.)
Answer: At first, you do negative work on the ball and extract energy from it: you push the ball away from you as it moves toward you. Your force and its movement are in opposite directions, so you do negative work on it and its energy decreases. As the ball rebounds, you still push it away from you but now it moves away from you as well. You do (positive) work on it and its energy increases.
Why: As you stop the ball, you are pushing that ball in the direction opposite its motion and taking energy out of it. As the ball picks up speed in the other direction, you are pushing it in the direction it is moving so you put energy into it.
4. The ball leaves your hand heading forward and downward at a furious pace. An instant before it reaches the floor on your opponent’s side, the ball is traveling even faster than when it left your hand and thus has more kinetic energy than you gave it. Where did its additional kinetic energy come from?
Answer: The ball has converted gravitational potential energy into additional kinetic energy.
Why: Once the ball leaves your hands, it is falling freely. It accelerates downward and picks up speed. Overall, its kinetic energy increases but at the expense of gravitational potential energy.
For your junior year abroad, you sign up for what sounds like a wonderful part-time job. You arrive at work, expecting to be a food-taster in a gourmet restaurant but are shocked to discover that your understanding of the local language is not as good as you thought. The words “lift,” “fork,” and “taster” suffered in their passage through your dictionary and you are saddened to find that you are now a “forklift tester.” Still, you decide to that it will probably be fun, particularly since your driving license was revoked for getting too many speeding tickets last year. You’re off to the races again!
5. You are taking a new forklift through its paces at the factory. You slide its blades under a heavy pallet of concrete and begin to raise that pallet off the floor. The pallet begins to accelerate upward, going from motionless to some upward velocity. During this starting time, (a) how does the force that the forklift exerts on the pallet compare to the pallet’s weight (amount: more, less, or same; direction: same or opposite) and (b) how does the force that the forklift exerts on the pallet compare to the force the pallet exerts on the forklift (amount: more, less, or same; direction: same or opposite)?
Answer: (a) The forklift pushes upward on the pallet with a force larger in amount than the pallet's downward weight. The forces are in opposite directions. (b) The forces that the forklift and pallet exert on one another are equal in amount but opposite in direction.
Why: To make the pallet accelerate upward, the forklift must more than balance the pallet's weight. It must push upward on the pallet hard enough to give the pallet an upward net force. The force that the forklift exerts on the pallet is larger in amount and opposite in direction compared to the pallet's weight. However, the pallet pushes back on the forklift with a force that is exact equal in amount but opposite in direction compared to the force that the forklift exerts on the pallet. Those last two forces are a Newton's third law pair (two objects pushing on one another) and must be equal but opposite.
6. Soon the pallet is rising upward at constant velocity. Is the forklift doing work on the pallet during this period? If so, where is the energy going as it enters the pallet?
Answer: Yes, the pallet is doing work and the energy is going into the pallet's gravitational potential energy.
The forklift is pushing upward on the pallet and the pallet is moving upward, so the forklift is doing work on the pallet. This energy is being stored in the gravitational forces between the earth and the pallet and is called gravitational potential energy.
7. You stop the pallet from rising and then start to drive forward. You find that the forklift responds much more slowly than it did before you picked up the heavy pallet. Explain why it’s so much harder for the forklift to gather speed now.
Answer: The loaded forklift has much more mass (inertia) and accelerates more slowly than before in response to a certain force.
Why: Adding mass to the forklift makes it harder to accelerate. You either need more force to achieve the same old acceleration or you'll have to live with less acceleration than before.
8. You have finally gotten the forklift moving at your favorite breakneck speed when the boss steps into your path. You slam on the brakes but the pallet flies forward and smashes on the floor. Needless to say, you are now unemployed but as least the boss wasn’t hurt. What propelled the pallet forward even though the forklift was stopping?
Answer: The pallet's inertia propelled it forward.
Why: No force acted on the pallet to keep it moving forward when the forklift stopped. It simply behaved in an inertial fashion. It coasted forward and slipped off the forklift.