Q: A force $$F$$ acts at an angle $$\theta to $$the displacement $$d. $$Which component of the force is responsible for doing work?

The component parallel to the displacement, $$F\cos\theta$$

Question 1

A centrifuge has a radius of 8 cm and rotates such that the acceleration experienced is $$116,000\,g. $$What is the period $$T of $$rotation in seconds?

Accepted Answer

$$T = \sqrt{\frac{4\pi^2$ r}{a_c}}$$

Question 2

A person pushes a crate 10.0 meters across the floor with a force of 74.0 N. How much work does he do?

Accepted Answer

$$W = 740\,J$$

Question 3

Which equation correctly defines the work done by a constant force at an angle $$	heta to $$the displacement?

Accepted Answer

$$W = Fd\cos	heta$$

Question 4

A waitress carries a 30.0-N tray at constant velocity for 4.0 meters across a restaurant. How much work does she do on the tray?

Accepted Answer

$$W = 0\,J$$

Question 5

A person pulls a wagon 28.0 meters with a 35.0-N force acting 48.0° above the horizontal. How much work is done by the force?

Accepted Answer

$$W = (35.0\cos48^\circ)(28.0) = 656\,J$$

Question 6

Which of the following best describes the unit 'joule'?

Accepted Answer

The amount of work required to exert a one-newton force over a distance of one meter.

Question 7

A 100.0-kg crate is pulled up a 30.0° incline for 6.00 meters with a tension of 835 N. What is the work done by the tension in the rope?

Accepted Answer

$$W = (835\,N)(6.00\,m)\cos0^\circ = 5010\,J$$

Question 8

If a force acts perpendicular to the displacement, what is the work done by the force?

Accepted Answer

$$W = 0$$

Question 9

A force-position graph shows a force of 5000 N acting over 7 m, then a force of -7000 N acting over 2 m. What is the total work done?

Accepted Answer

$$W = (5000\,N)(7\,m) + (-7000\,N)(2\,m) = 21,000\,J$$

Question 10

Which integral represents the work done by a variable force $$F$$ over a displacement from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F \cdot dx$$

Question 11

A force of 30 N acts vertically upward while a tray is carried horizontally for 4 m. What is the angle between the force and displacement, and what is the work done?

Accepted Answer

Angle is $$90^\circ$$, work is $$0\,J$$

Question 12

Which of the following statements about the law of conservation of energy is correct?

Accepted Answer

Energy cannot be created or destroyed, only transformed from one form to another.

Question 13

A force of 35 N is applied at an angle of $$48^\circ$$ above the horizontal to move a cart 28 m. What is the horizontal component of the force?

Accepted Answer

$$F_x = 35\cos48^\circ$$

Question 14

Which of the following is the correct expression for work done by gravity when moving an object down an incline of angle $$	heta$$?

Accepted Answer

$$W = F_g d \cos	heta$$

Question 15

If the angle between force and displacement is $$180^\circ$$, what is the value of $$\cos180^\circ$$ and what does it imply about the work done?

Accepted Answer

$$\cos180^\circ = -1$$, work is negative

Question 16

A force $$F$$ acts at an angle $$	heta to $$the displacement $$d. $$Which component of the force is responsible for doing work?

Accepted Answer

The component parallel to the displacement, $$F\cos	heta$$

Question 17

Which of the following is a correct real-world example of zero work being done?

Accepted Answer

Carrying a heavy box at constant height across a room

Question 18

Which formula would you use to calculate the work done by a variable force $$F(x)$$ over a displacement from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F(x) dx$$

Work and Rotational Motion in Physics: Concepts, Calculations, and Applications

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