Q: Which of the following is true about the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

$$\vec{A} \cdot \vec{B} = AB \cos \theta$$

Question 1

Which of the following statements about work is correct?

Accepted Answer

Work is a scalar quantity and its unit is the joule (J).

Question 2

A force $$\vec{F}$$ acts on an object causing a displacement $$\Delta \vec{r} at an $$angle $$	heta$$ between them. What is the correct formula for the work done by the force?

Accepted Answer

$$W = F \Delta r \cos 	heta$$

Question 3

Which of the following scenarios results in negative work being done on a system?

Accepted Answer

A force is applied opposite to the direction of the displacement.

Question 4

A block of mass $$m$$ slides on a horizontal surface with kinetic friction coefficient $$\mu_k. If it $$moves a distance $$d$$ before stopping, what is the increase in internal energy of the block-surface system?

Accepted Answer

$$\Delta E_{int} = \mu_k m g d$$

Question 5

Which of the following best describes the relationship between work and kinetic energy according to the work-kinetic energy theorem?

Accepted Answer

$$W = \Delta K$$

Question 6

A spring with spring constant $$k is $$compressed by a distance $$x. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} kx^2$

Question 7

A 15 kg mass is lifted vertically 12 m at constant speed. What is the work done by gravity?

Accepted Answer

$$W = -mgh$$

Question 8

Which statement about gravitational potential energy is correct?

Accepted Answer

It depends only on the vertical height above the reference point.

Question 9

A skier of mass $$m$$ moves up a slope inclined at angle $$	heta$$ with a tension $$T in $$the rope making an angle $$\alpha$$ with the slope. What is the work done by the tension force over a distance $$d$$?

Accepted Answer

$$W_T = T d \cos \alpha$$

Question 10

A block of mass $$m is $$projected toward a spring of constant $$k$$ with initial speed $$v. $$What is the maximum compression $$x_{max} of $$the spring when the block comes to rest?

Accepted Answer

$$x_{max} = \sqrt{\frac{mv^2$}{k}}$$

Question 11

Which of the following is true about the elastic potential energy stored in a spring?

Accepted Answer

It is zero when the spring is at its natural length.

Question 12

A person pushes a 40 kg box at constant speed over a horizontal surface with $$\mu_k = 0.2$$ for a distance of 6.5 m in 9 s. What is the power produced by the person?

Accepted Answer

$$P = \frac{\mu_k m g d}{t}$$

Question 13

Which of the following is the correct expression for instantaneous power delivered by a force $$\vec{F}$$ acting on an object with velocity $$\vec{v}$$?

Accepted Answer

$$P = \vec{F} \cdot \vec{v}$$

Question 14

If a block is released from rest at $$x = x_0$ and oscillates on a frictionless surface attached to a spring, what happens to its energy as it moves?

Accepted Answer

Elastic potential energy is converted to kinetic energy and vice versa.

Question 15

Which of the following is true about the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos 	heta$$

Question 16

A 1000 kg elevator is attached to an 1800 kg counterweight. What power must the motor provide to raise the elevator at 0.4 m/s?

Accepted Answer

$$P = (m_{elevator} - m_{counterweight}) g v$$

Question 17

Which of the following is NOT a way energy can be stored in a system as described in the study materials?

Accepted Answer

Thermal energy due to temperature change

Question 18

When a book slides to a stop on a rough surface, what happens to its kinetic energy?

Accepted Answer

It is converted entirely to internal energy (heat) of the book and surface.

Question 19

Which of the following is true about the reference configuration for gravitational potential energy?

Accepted Answer

It is arbitrary, but differences in potential energy are independent of the choice.

Chapter 7: Energy of a System – Physics for Scientists and Engineers

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