Q: An elevator of mass 1000 kg carries a load of 800 kg and moves upward at constant speed of 3 m/s. If a frictional force of 4000 N opposes the motion, what is the minimum power the motor must deliver?

$$P = (21600 \text{ N}) (3 \text{ m/s}) = 64800 \text{ W}$$

Question 1

A force $$F_x$$ acts on a particle as it moves along the x-axis from $$x_1 to$$ $$x_2. If$$ $$F_x$$ varies with position, how is the total work done by the force calculated?

Accepted Answer

By integrating the force over the displacement: $$W = \int_{x_1$}^{x_2$} F_x dx$$

Question 2

Which of the following statements about the work done by a spring force is correct?

Accepted Answer

The work done by a spring force is given by $$W_s = \frac{1}{2} k x^2$ if the spring is stretched from x=0$ to x=x$.

Question 3

A 0.40 kg canister slides across a frictionless counter at 0.50 m/s and compresses a spring with $$k = 750 N/m $$until it stops. What is the maximum compression $$d of $$the spring?

Accepted Answer

$$d = \sqrt{\frac{m v^2$}{k}}$$

Question 4

The area under the curve of a force vs. position graph represents:

Accepted Answer

The total work done by the force over the displacement.

Question 5

A balky cow is pushed with a force $$F_x = -[20.0 	ext{ N} + (3.0 	ext{ N/m})x]$$ from $$x=0 m to$$ $$x=6.90 m. $$What is the total work done by this force?

Accepted Answer

$$W = -209 	ext{ J}$$

Question 6

Which equation correctly expresses Hooke's Law for a spring?

Accepted Answer

$$F = -kx$$

Question 7

If you lift a 100 N barbell through a vertical distance of 1.0 m at constant velocity, how much work do you do?

Accepted Answer

$$100 	ext{ J}$$

Question 8

A force acting on a particle varies with $$x as $$shown in the figure: $$F_x = 5.0 N $$for $$0 \u003c x \u003c 4.0 m$$, then decreases linearly to zero at $$x = 6.0 m. $$What is the total work done from $$x=0 to$$ $$x=6.0 m$$?

Accepted Answer

$$25 	ext{ J}$$

Question 9

What is the SI unit of power?

Accepted Answer

Watt

Question 10

Which of the following best describes a kilowatt-hour (kWh)?

Accepted Answer

A unit of energy

Question 11

A 700 N marine climbs a 10.0 m vertical rope at a constant speed in 8.00 s. What is his power output?

Accepted Answer

$$875 	ext{ W}$$

Question 12

The work-kinetic energy theorem states that the net work done on a particle is equal to:

Accepted Answer

The change in its kinetic energy: $$W = \frac{1}{2} m v_f^2$ - \frac{1}{2} m v_i^2$

Question 13

An elevator of mass 1000 kg carries a load of 800 kg and moves upward at constant speed of 3 m/s. If a frictional force of 4000 N opposes the motion, what is the minimum power the motor must deliver?

Accepted Answer

$$P = (21600 	ext{ N}) (3 	ext{ m/s}) = 64800 	ext{ W}$$

Question 14

Which of the following is true about the work done by a constant force $$F$$ over a displacement $$x$$?

Accepted Answer

$$W = F \cdot x$$

Question 15

If Mike applies 10 N of force over 3 m in 10 seconds, and Joe applies the same force over the same distance in 1 minute, who did more work?

Accepted Answer

Both did the same work

Question 16

Mike performed 5 J of work in 10 seconds, Joe did 3 J of work in 5 seconds. Who produced the greater power?

Accepted Answer

Joe produced more power

Question 17

The average power delivered by a force $$F$$ moving an object at average velocity $$\vec{v} is $$given by:

Accepted Answer

$$P_{avg} = F \cdot \vec{v}$$

Question 18

Which of the following best describes the spring constant $$k$$?

Accepted Answer

It measures the stiffness of the spring.

Question 19

If a spring is stretched from $$x_i = 0 to$$ $$x_f = x$$, what is the work done by the spring force?

Accepted Answer

$$W_s = -\frac{1}{2} k x^2$

Work and Kinetic Energy: Study Notes (Chapter 6)

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