Q: If you lift two identical boxes, each weighing 50 N, to a height of 2 meters, how much work have you done in total?

$$W = 2 \times 50 \text{ N} \times 2 \text{ m} = 200 \text{ J}$$

Q: What is the SI unit of work, and how is it defined?

Joule (J), defined as $$1 \text{ J} = 1 \text{ N} \cdot 1 \text{ m}$$

Q: If a force varies with position as $$F(x) = 3x$$, what is the work done as the object moves from $$x = 0 to$$ $$x = 2$$ meters?

$$W = \$$int_0$$^2 3x \, dx = 6 \text{ J}$$

Question 1

Which of the following best describes the physical definition of work in physics?

Accepted Answer

Work is the product of a constant force $$F$$ and the displacement $$s in $$the direction of the force: $$W = F s$$

Question 2

A person pushes against a stationary brick wall for several minutes. What is the work done on the wall?

Accepted Answer

Zero, because the wall does not move and $$W = F s$$ requires displacement.

Question 3

If you lift two identical boxes, each weighing 50 N, to a height of 2 meters, how much work have you done in total?

Accepted Answer

$$W = 2 	imes 50 	ext{ N} 	imes 2 	ext{ m} = 200 	ext{ J}$$

Question 4

Which of the following statements about work is correct?

Accepted Answer

Work is a scalar quantity and can be positive, zero, or negative.

Question 5

What is the SI unit of work, and how is it defined?

Accepted Answer

Joule (J), defined as $$1 	ext{ J} = 1 	ext{ N} \cdot 1 	ext{ m}$$

Question 6

A block of weight 100 N is lifted using a pulley system that reduces the required force to 33.3 N. What is the trade-off in this scenario?

Accepted Answer

The force required is reduced, but the distance over which the force is applied increases.

Question 7

A car accelerates as a result of a force applied in the direction of its motion. What is the sign of the work done on the car?

Accepted Answer

Positive, because energy is added to the system ($$W \u003e 0).$$

Question 8

A package of mass $$m$$ slides down a frictionless ramp inclined at angle $$	heta$$ from a height $$h. $$What is the total work done by all forces on the package as it reaches the bottom?

Accepted Answer

$$W = m g h$$

Question 9

How is the work done by a variable force, such as stretching a spring, calculated?

Accepted Answer

By finding the area under the force vs. displacement graph: $$W = \int F(x) \, dx$$

Question 10

A spring obeys Hooke's law, $$F = kx. $$What is the work required to stretch the spring from $$x = 0 to$$ $$x = X$$?

Accepted Answer

$$W = \frac{1}{2} k X^2$

Question 11

Which scenario results in negative work being done on an object?

Accepted Answer

A force acts opposite to the direction of displacement.

Question 12

If a force varies with position as $$F(x) = 3x$$, what is the work done as the object moves from $$x = 0 to$$ $$x = 2$$ meters?

Accepted Answer

$$W = \$$int_0$$^2 3x \, dx = 6 	ext{ J}$$

Question 13

Which of the following is NOT a correct statement about work?

Accepted Answer

Work is always positive.

Question 14

A force of 10 N is applied at an angle of $$60^\circ to $$the direction of displacement of 5 m. What is the work done?

Accepted Answer

$$W = 10 	imes 5 	imes \cos 60^\circ = 25 	ext{ J}$$

Question 15

Which of the following best explains why energy considerations can simplify calculations in physics?

Accepted Answer

Energy is conserved in many systems, allowing us to avoid detailed force analysis.

Question 16

A person uses a slingshot to launch a stone. Which type of work is primarily involved in stretching the slingshot?

Accepted Answer

Work done by a variable force, as the tension increases with displacement.

Question 17

If the force applied to an object is perpendicular to its displacement, what is the work done?

Accepted Answer

$$W = F s \cos 90^\circ = 0$$

Question 18

Which historical figure is known for pioneering work in thermodynamics and the concept of work?

Accepted Answer

James Prescott Joule

Question 19

When lifting a block vertically at constant speed, what is the minimum tension required in the string?

Accepted Answer

Equal to the weight of the block: $$T = mg$$

Work and Energy – Chapter 7 Study Notes

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