Question 1

A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 908 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?

Accepted Answer

Work done = Force × Distance × cos(angle)908 J = Tension × 15 m × cos(36°)Tension = 908 J / (15 m × cos(36°))Tension ≈ 75 N

Question 2

You carry a 7.0 kg bag of groceries 1.2 m above the level floor at a constant velocity of 75 cm/s across a room that is 2.3m room. How much work do you do on the bag in the process?

Accepted Answer

Work done on an object is given by the formula W = Fd, where W is work, F is force, and d is distance. Since the bag is moving at constant velocity, there is no net force acting on it. Therefore, the work done on the bag is zero, regardless of the distance it is moved. Thus the correct answer is A) 0.0 J.

Question 3

An airplane flies 120 km at a constant altitude in a direction 30.0° north of east. A wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kN in a direction 10.0° south of west. How much work is done on the plane by the air?

Accepted Answer

The work done by the air on the plane is equal to the negative of the scalar product of the force due to the air and the displacement of the plane. The force due to the air is given by:$$\overrightarrow{F} = (2.40 	ext{ kN}) \left[ \cos(180^\circ + 10.0^\circ) \hat{i} + \sin(180^\circ + 10.0^\circ) \hat{j} ight] = (-2.36 	ext{ kN}) \hat{i} + (0.414 	ext{ kN}) \hat{j}$$The displacement of the plane is given by:$$\overrightarrow{d} = (120 	ext{ km}) \left[ \cos(30.0^\circ) \hat{i} + \sin(30.0^\circ) \hat{j} ight] = (103.9 	ext{ km}) \hat{i} + (60.0 	ext{ km}) \hat{j}$$The work done by the air on the plane is then:$$W = \overrightarrow{F} \cdot \overrightarrow{d} = (-2.36 	ext{ kN})(103.9 	ext{ km}) + (0.414 	ext{ kN})(60.0 	ext{ km}) = -2.71 	imes 10^8 	ext{ J}$$

Question 4

A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do?

Accepted Answer

The answer of A student slides her 80.0-kg desk across...

Question 5

A 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping?

Accepted Answer

The distance traveled by each object before coming to a stop depends only on their initial speed and the magnitude of the braking force acting on them. Both objects encounter the same force, so they decelerate at the same rate. Thus, they will travel the same distance before coming to a stop.

Question 6

Which of the graphs in the figure represents a spring that gets less stiff the more it is stretched?

Accepted Answer

The answer of Which of the graphs in the figure...

Question 7

An object is acted upon by a force that represented by the force vs. position graph in the figure. What is the work done as the object moves
(a) from 4 m to 6 m?
(b) from 6 m to 12 m?

Accepted Answer

The answer of An object is acted upon by a...

Question 8

In the figure, a 700-kg crate is on a rough surface inclined at 30°. A constant external force P = 5600 N is applied horizontally to the crate. As the force pushes the crate a distance of 3.00 m up the incline, the speed changes from 1.40 m/s to 2.50 m/s. How much work does gravity do on the crate during this process?

Accepted Answer

The answer of In the figure, a 700-kg crate is...

Question 9

Find the net work done by friction on the body of a snake slithering in a complete circle of 3.93 m radius. The coefficient of friction between the ground and the snake is 0.25, and the snake's weight is 54.0 N.

Accepted Answer

The net work done by friction is negative because the force of friction opposes the motion of the snake. The magnitude of the work done by friction is equal to the product of the force of friction and the distance traveled by the snake. The force of friction is equal to the coefficient of friction times the normal force, which is equal to the weight of the snake. The distance traveled by the snake is equal to the circumference of the circle, which is 2πr. Therefore, the net work done by friction is:$$W_f = -f*d = -μ*N*2πr = -0.25*54.0 N*2π*3.93 m = -330 J$$

Question 10

Which of the graphs in the figure illustrates Hooke's Law?

Accepted Answer

The answer of Which of the graphs in the figure...

Question 11

In the figure, a constant external force P = 160 N is applied to a 20.0-kg box, which is on a rough horizontal surface. While the force pushes the box a distance of 8.00 m, the speed changes from 0.500 m/s to 2.60 m/s. The work done by friction during this process is closest to

Accepted Answer

The answer of In the figure, a constant external force...

Question 12

If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy.

Accepted Answer

This is because the work done by a force on an object is given by the dot product of the force and the displacement of the object. If the force is always perpendicular to the direction of motion, then the dot product is zero and no work is done on the object. Therefore, the kinetic energy of the object remains constant.

Question 13

A crane lifts a 425 kg steel beam vertically a distance of 117 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

Accepted Answer

Work done by the crane is equal to the change in kinetic energy of the beam.$$	ext{Work done}=\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2$$$$=\frac{1}{2}(425	ext{ kg})(1.8	ext{ m/s})^2-0$$$$=5.8	imes10^5	ext{ J}$$

Question 14

Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring. The slope of the curve would be

Accepted Answer

The slope of the displacement vs. applied force plot for an ideal elastic spring is the reciprocal of the spring constant, according to Hooke's Law (F = kx), where k is the spring constant.

Question 15

A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end. The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball. As the ball swings from its lowest point to its highest point

Accepted Answer

The work done by gravity can be calculated using the formula $W = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $h$ is the height change, which is $2.00 m$ in this case. Thus, $W = 3.00 \times 9.8 \times 2.00 = 58.8 \times 2 = 117.6 J$, which rounds to $-118 J$ when considering the direction (upward against gravity). The tension in the string does no work because it acts perpendicular to the displacement of the ball at all points in its path, meaning the force vector of tension and the displacement vector are orthogonal, resulting in zero work done by tension.

Question 16

A stock person at the local grocery store has a job consisting of the following five segments:
(1) picking up boxes of tomatoes from the stockroom floor
(2) accelerating to a comfortable speed
(3) carrying the boxes to the tomato display at constant speed
(4) decelerating to a stop
(5) lowering the boxes slowly to the floor.
During which of the five segments of the job does the stock person do positive work on the boxes?

Accepted Answer

Positive work is done when the force applied to an object is in the direction of the object's displacement. In segment (1), lifting the boxes off the floor involves applying a force upward, which is in the direction of the boxes' displacement, thus doing positive work. In segment (2), accelerating to a comfortable speed also involves applying a force in the direction of the boxes' motion, doing positive work. Segments (3), (4), and (5) involve either no work in the case of constant speed (since there's no acceleration) or work that does not contribute to the boxes' displacement in the desired direction, such as decelerating or lowering the boxes.

Question 17

A graph of the force on an object as a function of its position is shown in the figure. Determine the amount of work done by this force on an object that moves from x = 1.0 m to x = 6.0 m. (Assume an accuracy of 2 significant figures for the numbers on the graph.)

Accepted Answer

The answer of A graph of the force on an...

Question 18

Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do.

Accepted Answer

Work is defined as the product of force and displacement in the direction of the force. Since the wall does not move, there is no displacement, and therefore, no work is done by either Joel or Jerry, regardless of the time spent pushing.

Question 19

Three forces, F₁ = 20.0 N, F₂ = 40.0 N, and F₃ = 10.0 N act on an object with a mass of 2.00 kg which can move along a frictionless inclined plane as shown in the figure. The questions refer to the instant when the object has moved through a distance of 0.600 m along the surface of the inclined plane in the upward direction. Calculate the amount of work done by (a) F₁ (b) F₂ (c) F₃.

Accepted Answer

The answer of Three forces, F₁ = 20.0 N, F₂...

Question 20

Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. When they hit the ground

Accepted Answer

The answer of Two objects, one of mass m and...

Quiz 6: Work and Kinetic Energy