# Dynamics

## Problems

### practice

- 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.
- Draw a free body diagram showing all the forces acting on the cheeseburger.
- Determine the weight of the cheeseburger.
- Determine the
*magnitude*and*direction*of the net force on the cheeseburger. - Determine the
*magnitude*and*direction*of the elevator's acceleration. - 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.

- 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).
- Draw a free body diagram of the goose in flight.
- Determine the following quantities for the goose in flight…
- its acceleration
- its weight
- the magnitude and direction of the net force acting on it
- the magnitude of the upward lift provided by its wings
- the magnitude of the forward thrust provided by its wings

- 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…
- the acceleration?
- the weight?
- the net force?
- the lift?
- 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.

- A laboratory cart (
*m*_{1}= 500 g) is pulled horizontally across a level track by a lead weight (*m*_{2}= 25 g) suspended vertically off the end of a pulley as shown in the diagram below. (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…
- the cart
- the weight

- Determine…
- the acceleration of the system
- the tension in the string

- Draw a free body diagram for…
- Write something completely different.

### conceptual

- 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*.- Draw a free body diagram showing all the forces acting on the book.
- What is the weight of the book?
- What is the acceleration of the book?
- What is the net force on the book?
- What is the normal force of the table on the book?
- What is the normal force of the book on the table?

- 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*.- Draw a free body diagram showing all the forces acting on the book.
- What is the weight of the book?
- What is the acceleration of the book?
- What is the net force on the book?
- Is the speed of the book increasing, decreasing, or constant?
- Is the acceleration of the book increasing, decreasing, or constant?

### numerical

- An open parachute provides an upward drag force of 855 N to a 56 kg skydiver.
- Draw a free body diagram showing all the forces acting on the skydiver.
- Determine the weight of the skydiver.
- Determine the
*magnitude*and*direction*of the net force on the skydiver. - Determine the
*magnitude*and*direction*of the skydiver's acceleration. - Determine the speed of the skydiver ten seconds after the parachute opened if her initial velocity was 60 m/s.

- During lift off, the mass of a fully loaded space shuttle is 2.0 × 10
^{6}kg. The total thrust provided by the three main engines and two solid rocket boosters is 4.1 × 10^{7}N. Drag*is not*significant.- Draw a free body diagram showing all the forces acting on the space shuttle.
- Determine the weight of the shuttle.
- Determine the
*magnitude*and*direction*of the net force on the shuttle. - Determine the
*magnitude*and*direction*of the shuttle's acceleration. - Determine the speed of the shuttle ten seconds after liftoff if its acceleration remains constant.

- A raindrop of mass 2.4 × 10
^{−4}kg falls with an acceleration of 1.2 m/s^{2}down. Drag*is*- Draw a free body diagram showing all the forces acting on the raindrop.
- Determine the weight of the raindrop.
- Determine the
*magnitude*and*direction*of the net force on the raindrop. - Determine the
*magnitude*and*direction*of the drag force acting on the raindrop. - Determine the distance traveled by the raindrop in two seconds if its initial velocity is 8.0 m/s.

- A 2,000 kg car is driving forward on a freeway at 30 m/s. It accelerates forward at a constant 1.6 m/s
^{2}for 4.0 s. The tires push the car forward with 4,000 N of force. Air resistance*is*significant, but other types of friction are not.- Draw a free body diagram showing all the forces acting on the car.
- Determine the weight of the car.
- Determine the
*magnitude*and*direction*of the net force on the car. - Determine the
*magnitude*and*direction*of the air resistance acting of the car. - Determine the distance the car traveled during the 4.0 s interval.

- A 2,000 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.- Draw a free body diagram showing all the forces acting on the car.
- Determine the weight of the car.
- Determine the
*magnitude*and*direction*of the net force on the car. - Determine the
*magnitude*and*direction*of the car's acceleration. - Is the speed of the car increasing, decreasing, or remaining constant in this problem? Justify your answer?

- The T-38 Talon is a small (14 × 4 × 8 m), lightweight (4,000 kg), twin-engine, high-altitude, supersonic jet used by various US Department of Defense groups and NASA for training purposes.
- A T-38 requires 6,670 N of thrust to fly at a constant horizontal velocity 300 m/s. Determine the following quantities for the T-38 at this moment…
- the weight
- the lift provided by the wings
- the aerodynamic drag

- The pilot has been instructed to accelerate horizontally at 0.10 g. Determine…
- the new thrust of the engines (assuming the drag remains constant)
- the time it takes to reach 360 m/s

- A T-38 requires 6,670 N of thrust to fly at a constant horizontal velocity 300 m/s. Determine the following quantities for the T-38 at this moment…
- A group of students in a physics class set up the experiment shown in the diagram below. A laboratory cart (
*m*_{1}= 500 g) on a level track is connected by a horizontal string that runs over a pulley to a vertically suspended lead weight (*m*_{2}= 25 g). Friction on the cart is not negligible in this experiment. (Assume the string and pulley contribute negligible mass to the system, however.)- Draw a free body diagram for…
- the lab cart
- the lead weight

- The students first use a cart with sticky wheels and nothing moves. Determine…
- the weight of the lead weight
- the tension in the string connecting the weight to the cart
- the friction force acting on the cart

- 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/s
^{2}. Determine…- the tension in the string
- the new friction force acting on the cart

- Draw a free body diagram for…

### algebraic

- A kind of Atwood's machine is built from two cylinders of mass
*m*_{1}and*m*_{2}; a cylindrical pulley of mass*m*_{3}and radius*r*; a light, frictionless axle; and a piece of light, unstretchable string. The heavier mass*m*_{1}is held above the floor a height*h*and then relased from rest.- Draw a free body diagram showing all the forces acting on…
- the heavier mass
- the lighter mass

- Determine…
- the acceleration of the system
- the tension in the string
- the time it takes for the heavier mass to reach the floor
- the speed of the system when the heavier mass hits the floor

- Draw a free body diagram showing all the forces acting on…