The Physics
Hypertextbook
Opus in profectus

# Dynamics

## Problems

### practice

1. A person stands in an elevator weighing a cheeseburger with a kitchen scale. (It could happen.) The mass of the cheeseburger is 0.150 kg. The scale reads 1.14 N.
1. Draw a free body diagram showing all the forces acting on the cheeseburger.
2. Determine the weight of the cheeseburger.
3. Determine the magnitude and direction of the net force on the cheeseburger.
4. Determine the magnitude and direction of the elevator's acceleration.
5. At the time the person in the elevator is weighing the cheeseburger, the elevator's instantaneous velocity is upward. Is the speed of the elevator increasing, decreasing, or remaining constant at this moment? Justify your answer.
2. A 4.5 kg Canada goose is about to take flight. It starts from rest on the ground, but after a single step it is completely airborne. After 2.0 s of horizontal flight the bird has reached a speed of 6.0 m/s (fast enough to stay aloft, but not so fast that we need to worry about air resistance… at first).
1. Draw a free body diagram of the goose in flight.
2. Determine the following quantities for the goose in flight…
1. its acceleration
2. its weight
3. the magnitude and direction of the net force acting on it
4. the magnitude of the upward lift provided by its wings
5. the magnitude of the forward thrust provided by its wings
3. Any object moving through the air will experience air resistance. We just decided to ignore it temporarily. If we now admit that air resistance was present to some extent, how will this change the computed values of…
1. the acceleration?
2. the weight?
3. the net force?
4. the lift?
5. the thrust?
• All the measurements given in the problem are still valid for part c of this problem. The mass is still 4.5 kg and the bird still accelerates from rest to 6.0 m/s in 2.0 s.
3. A laboratory cart (m1) rests on a level track. It is connected to a lead weight (m2) suspended vertically off the end of a pulley as shown in the diagram below. The system is released and the cart accelerates to the right. (Assume the string and pulley contribute negligible mass to the system and that friction is kept low enough to be ignored.) Draw a free body diagram for…
1. the laboratory cart
Determine…
1. the acceleration of the system
2. the tension in the string
4. Write something completely different.

### conceptual

1. Answer the following questions about a 1 kg book that is resting 1 m above the floor on a level, 10 kg table. For all numerical answers, state both magnitude and direction.
1. Draw a free body diagram showing all the forces acting on the book.
2. What is the weight of the book?
3. What is the acceleration of the book?
4. What is the net force on the book?
5. What is the normal force of the table on the book?
6. What is the normal force of the book on the table?
2. Answer the following questions about a 1 kg book that is falling freely from a 1 m tall, 10 kg table. For all numerical answers, state both magnitude and direction.
1. Draw a free body diagram showing all the forces acting on the book.
2. What is the weight of the book?
3. What is the acceleration of the book?
4. What is the net force on the book?
5. Is the speed of the book increasing, decreasing, or constant?
6. Is the acceleration of the book increasing, decreasing, or constant?

### numerical

1. An open parachute provides an upward drag force of 855 N to a 56 kg skydiver.
1. Draw a free body diagram showing all the forces acting on the skydiver.
2. Determine the weight of the skydiver.
3. Determine the magnitude and direction of the net force on the skydiver.
4. Determine the magnitude and direction of the skydiver's acceleration.
5. Determine the speed of the skydiver ten seconds after the parachute opened if her initial velocity was 60 m/s.
2. During lift off, the mass of a fully loaded space shuttle is 2.0 × 106 kg. The total thrust provided by the three main engines and two solid rocket boosters is 4.1 × 107 N. Drag is not significant.
1. Draw a free body diagram showing all the forces acting on the space shuttle.
2. Determine the weight of the shuttle.
3. Determine the magnitude and direction of the net force on the shuttle.
4. Determine the magnitude and direction of the shuttle's acceleration.
5. Determine the speed of the shuttle ten seconds after liftoff if its acceleration remains constant.
3. A raindrop of mass 2.4 × 10−4 kg falls with an acceleration of 1.2 m/s2 down. Drag is significant in this problem.
1. Draw a free body diagram showing all the forces acting on the raindrop.
2. Determine the weight of the raindrop.
3. Determine the magnitude and direction of the net force on the raindrop.
4. Determine the magnitude and direction of the drag force acting on the raindrop.
5. Determine the distance traveled by the raindrop in two seconds if its initial velocity is 8.0 m/s.
4. A 2000 kg car is driving forward on a freeway at 30 m/s. It accelerates forward at a constant 1.6 m/s2 for 4.0 s. The tires push the car forward with 4000 N of force. Air resistance is significant, but other types of friction are not.
1. Draw a free body diagram showing all the forces acting on the car.
2. Determine the weight of the car.
3. Determine the magnitude and direction of the net force on the car.
4. Determine the magnitude and direction of the air resistance acting of the car.
5. Determine the distance the car traveled during the 4.0 s interval.
5. A 2000 kg car is driving forward on a freeway at 30 m/s. The tires push the car forward with 600 N of force and air resistance pushes the car backward with 900 N of force. Air resistance is significant, but other types of friction are not.
1. Draw a free body diagram showing all the forces acting on the car.
2. Determine the weight of the car.
3. Determine the magnitude and direction of the net force on the car.
4. Determine the magnitude and direction of the car's acceleration.
5. Is the speed of the car increasing, decreasing, or remaining constant in this problem? Justify your answer?
6. The T-38 Talon is a small (14×4×8 m), lightweight (4000 kg), twin-engine, high-altitude, supersonic jet used by various US Department of Defense groups and NASA for training purposes.
1. A T-38 requires 6670 N of thrust to fly at a constant horizontal velocity 300 m/s. Determine the following quantities for the T-38 at this moment…
1. the weight
2. the lift provided by the wings
3. the aerodynamic drag
2. The pilot has been instructed to accelerate horizontally at 0.10 g. Determine…
1. the new thrust of the engines (assuming the drag remains constant)
2. the time it takes to reach 360 m/s
7. A group of students in a physics class set up the experiment shown in the diagram below. A laboratory cart (m1 = 500 g) on a level track is connected by a horizontal string that runs over a pulley to a vertically suspended lead weight (m2 = 25 g). Friction on the cart is not negligible in this experiment. (Assume the string and pulley contribute negligible mass to the system, however.) 1. Draw a free body diagram for…
1. the lab cart
2. The students first use a cart with sticky wheels and nothing moves. Determine…
1. the weight of the lead weight
2. the tension in the string connecting the weight to the cart
3. the friction force acting on the cart
3. The students find a small piece of debris lodged in one of the wheels and remove it. This reduces the fiction, but not to the point where it can be ignored. They perform the experiment and measure an acceleration of 0.40 m/s2. Determine…
1. the tension in the string
2. the new friction force acting on the cart
8. ZARM! Despite my addition of an exclamation point, it's not an onomatopoeic sound effect from a comic book. Das Zentrum für Angewandte Raumfahrttechnologie und Mikrogravitation (or in English, the Center for Applied Space Technology and Microgravity) is a research institute at the University of Bremen in Germany that studies space technology and other sciences as they relate to gravity. The most prominent structure at this facility is the nearly 150 meter tall drop tower. Gravity is a fundamental force that acts on all objects everywhere in the universe. While it is impossible to eliminate gravity, its effects on systems can be reduced during free fall — a state often described as weightlessness, but that scientists prefer to call microgravity. In any case, when gravity gets turned off, things get interesting. At ZARM, scientists can choose between one of two different flight campaigns in the drop tower. The first is "drop mode" — a straight free fall.

During a simple drop experiment, the capsule is pulled up to a height of 120 meters to the top of the drop tube and then released. After 4.74 seconds the experiment has landed safely in the deceleration unit filled with polystyrene pellets. Before the experiment, 18 high-performance pumps make sure that the drop tube is almost free of air containing only one ten thousandth of the normal air pressure. Due to the vacuum, the air drag is so low that the Bremen Drop Tower can provide one of the best quality of microgravity — in some aspects even better than on the International Space Station (ISS). Therefore, ZARM's drop tower facility is a very economic and easily accessible alternative to doing research in space.

ZARM, 2020

Answer the following questions about a drop mode experiment using the information provided in the extended quote above. (Let the mass of the capsule be 500 kg.)
1. What is the speed of the capsule just before it impacted the deceleration unit?
2. What is the magnitude of the acceleration of the capsule in the deceleration unit if it stops in 8 m?
3. What is the weight of the capsule in newtons?
4. What is the magnitude of the net force on the capsule while it is traveling through the deceleration unit?
5. What is the magnitude of the force applied by the polystyrene pellets to the capsule while it is being decelerated?
The second type of flight campaign is "catapult mode", where the capsule is thrown vertically up from the bottom and then caught when it returns.

The pneumatically driven system takes 0.25 seconds to accelerate the experiment capsule to a speed of 168 kilometers per hour. The exact force of acceleration is being calculated for each individual experiment in order to throw the drop capsule as close as possible to the top of the drop tube and thus maximize the duration of the flight. After a couple of seconds the deceleration unit has already been moved into place again in order to catch the capsule on its way down.

ZARM, 2020

Answer the following questions about a catapult mode experiment using the information provided in the extended quote above. (Let the mass of the capsule be 400 kg.)
1. What is the launch speed of the capsule in meters per second?
2. What is the magnitude of the acceleration of the capsule while it is being pushed up by the catapult?
3. What is the weight of the capsule in newtons?
4. What is the magnitude of the net force on the capsule while it is being pushed up by the catapult?
5. What is the magnitude of the force applied by the catapult to the capsule while it is being pushed up?

### algebraic

1. A kind of Atwood's machine is built from two cylinders of mass m1 and m2; a massless cylindrical pulley; a light, frictionless axle; and a piece of light, unstretchable string. The heavier mass m1 is held above the floor a height h and then relased from rest.
1. Draw a free body diagram showing all the forces acting on…
1. the heavier mass
2. the lighter mass
2. Determine…
1. the acceleration of the system
2. the tension in the string
3. the time it takes for the heavier mass to reach the floor
4. the speed of the system when the heavier mass hits the floor