Question 1

A 3.0-kg brick rests on a perfectly smooth ramp inclined at 34° above the horizontal. The brick is kept from sliding down the plane by an ideal spring that is aligned with the surface and attached
To a wall above the brick. The spring has a spring constant (force constant) of 120 N/m. By how
Much does the spring stretch with the brick attached?
A) 24 cm
B) 240 cm
C) 14 cm
D) 36 cm
E) 360 cm

Accepted Answer

To find the stretch in the spring, we first calculate the force acting along the incline due to gravity, which is $F = mg\sin(\theta)$, where $m = 3.0 \, \text{kg}$, $g = 9.8 \, \text{m/s}^2$, and $\theta = 34^\circ$. This force is balanced by the spring force, $F_{\text{spring}} = kx$, where $k = 120 \, \text{N/m}$ and $x$ is the stretch in the spring. Setting these forces equal gives $mg\sin(\theta) = kx$. Solving for $x$ gives $x = \frac{mg\sin(\theta)}{k}$. Substituting the given values, $x = \frac{(3.0)(9.8)\sin(34^\circ)}{120}$ results in approximately $0.14 \, \text{m}$ or $14 \, \text{cm}$.

Question 2

An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant) of the spring is  45 N/m and the spring is stretched by  0.88 m when the object is accelerating at $1.4 \mathrm {~m} / \mathrm { s } ^ { 2 }$
what is the mass of the object?
A)  31 kg
B)  36 kg
C)  24 kg
D)  28 kg

Accepted Answer

The force exerted by the spring can be calculated using Hooke's Law, $F = kx$, where $k = 45 \, \text{N/m}$ is the spring constant and $x = 0.88 \, \text{m}$ is the stretch. So, $F = 45 \times 0.88 = 39.6 \, \text{N}$. Using Newton's second law, $F = ma$, where $a = 1.4 \, \text{m/s}^2$ is the acceleration, we can find the mass $m$ by rearranging the equation to $m = \frac{F}{a} = \frac{39.6}{1.4} = 28.29 \, \text{kg}$, which rounds to $28 \, \text{kg}$.

Question 3

You carry a 7.0-kg bag of groceries 1.2 m above the ground at constant speed across a 2.7 m room. How much work do you do on the bag in the process?
A) 157 J
B) 0.00 J
C) 185 J
D) 82 J

Accepted Answer

Work done is defined as the force applied to an object times the distance over which it's applied in the direction of the force. Since the bag is carried at a constant height and speed, the force you apply (upwards) is equal and opposite to the force of gravity, and there is no displacement in the direction of the force (up or down). The displacement is horizontal, so no work is done against gravity.

Question 4

A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pulls
horizontally on an 18-kg box that is resting on a horizontal floor. The coefficient of static
friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45.
(a) How long is the spring just as the box is ready to move?
(b) If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long
is the spring?
(c) How long is the spring if it pulls the box forward at a constant 2.75 m/s?

Accepted Answer

The answer of A very light ideal spring with a...

Question 5

How much work would a child do while pulling a 12-kg wagon a distance of 4.3 m with a 22 N force?
A) 95 J
B) 67 J
C) 52 J
D) 109 J

Accepted Answer

The work done is calculated using the formula Work = Force x Distance. Here, the force is 22 N and the distance is 4.3 m. So, Work = 22 N * 4.3 m = 94.6 J, which rounds to 95 J.

Question 6

It requires 0.30 kJ of work to fully drive a stake into the ground. If the average resistive force on the stake by the ground is 828 N, how long is the stake?
A) 0.41 m
B) 0.23 m
C) 0.36 m
D) 0.31 m

Accepted Answer

The answer of It requires 0.30 kJ of work to...

Question 7

An ornament of mass  40.0 g is attached to a vertical ideal spring with a force constant (spring constant) of  20.0 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?
A)  0.0816 m
B)  0.00200 m
C)  0.0196 m
D)  0.800 m
E)  0.200 m

Accepted Answer

The spring stretch ($x$) can be found using Hooke's Law, which states $F = kx$, where $F$ is the force applied, $k$ is the spring constant, and $x$ is the displacement of the spring from its equilibrium position. The force applied by the ornament due to gravity is its weight, $F = mg$, where $m$ is the mass of the ornament and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Substituting the weight into Hooke's Law gives $mg = kx$. Rearranging for $x$ gives $x = \frac{mg}{k}$. Substituting $m = 0.04 \, \text{kg}$, $g = 9.8 \, \text{m/s}^2$, and $k = 20.0 \, \text{N/m}$ gives $x = \frac{0.04 \times 9.8}{20.0} = 0.0196 \, \text{m}$.

Question 8

Matthew pulls his little sister Sarah along the horizontal ground in a wagon. He exerts a force on the wagon of  60.0 N at an angle of $37.0 ^ { \circ }$ above the horizontal. If he pulls her a distance of  12.0 m, how much work does Matthew do?
A)  185 J
B)  575 J
C)  433 J
D)  720 J

Accepted Answer

The answer of Matthew pulls his little sister Sarah along...

Question 9

A very light ideal spring having a spring constant (force constant) of  8.2 N/cm is used to lift a 2.2-kg tool with an upward acceleration of $3.25 \mathrm {~m} / \mathrm { s } ^ { 2 }$

If the spring has negligible length when it us not stretched, how long is it while it is pulling the tool upward?

Accepted Answer

The answer of A very light ideal spring having a...

Question 10

A  30-N box is pulled upward  6.0 m along the surface of a ramp that rises at $37 ^ { \circ }$ above the horizontal. How much work does gravity do on the box during this process?
A)  -110 J
B)  -140 J
C)  -1100 J
D)  -180 J
E)  120 J

Accepted Answer

The work done by gravity is calculated using the formula $W = -mgd \cos(\theta)$, where $m$ is the mass, $g$ is the acceleration due to gravity (9.8 m/s$^2$), $d$ is the distance moved, and $\theta$ is the angle of the incline. Here, the force due to gravity (weight) is given as 30 N, so $m = 30/g$, and $d = 6.0$ m, $\theta = 37^\circ$. Substituting these values, we find $W = -30 \times 6 \times \cos(37^\circ)$, which approximates to -110 J.

Question 11

Find the net work done by friction on a box that moves in a complete circle of radius  1.82 m on a uniform horizontal floor. The coefficient of kinetic friction between the floor and the box is  0.25 , and the box weighs  65.0 N
A)  1800 J
B)  370 J
C)  0 J
D)  190 J

Accepted Answer

The answer of Find the net work done by friction...

Question 12

A very light ideal spring of spring constant (force constant) 2.5 N/cm is 15 cm long when
nothing is attached to it. It is now used to pull horizontally on a 12.5-kg box on a perfectly
smooth horizontal floor. You observe that the box starts from rest and moves 96 cm during
the first 1.6 s of its motion with constant acceleration. How long is the spring during this
motion?

Accepted Answer

The answer of A very light ideal spring of spring...

Question 13

A force of 30 N stretches a very light ideal spring 0.73 m from equilibrium. What is the force constant (spring constant) of the spring?
A) 34 N/m
B) 22 N/m
C) 46 N/m
D) 41 N/m

Accepted Answer

The answer of A force of 30 N stretches a...

Question 14

A very light ideal spring stretches by 21.0 cm when it is used to hang a 135-N object. What is the weight of a piece of electronic equipment that would stretch the spring by 44.9 cm if you hung the
Equipment using the spring?
A) 289 N
B) 176 N
C) 405 N
D) 63 N

Accepted Answer

The spring constant k can be calculated using Hooke's Law: F = kx. For the 135-N object, k = 135 N / 0.21 m. For the electronic equipment, using the same spring constant, F = k * 0.449 m. Solving gives F = 289 N.

Question 15

A person carries a  25.0-N rock through the path shown in the figure, starting at point  A and ending at point  B . The total time from  A  to  B  is  1.50 min. How much work did gravity do on the rock between  A  and  B  ?

A)  75 J
B)  0 J
C)  275 J
D)  625 J
E)  20.0 J

Accepted Answer

The answer of A person carries a  25.0-N rock...

Question 16

A child does 350 J of work while pulling a box from the ground up to his tree house at a steady speed with a light rope. The tree house is 4.0 m above the ground. What is the mass of the box?
A) 5.3 kg
B) 6.7 kg
C) 8.9 kg
D) 8.0 kg

Accepted Answer

The work done (350 J) is equal to the gravitational potential energy gained by the box, which is mgh. Using the formula: 350 J = m * 9.8 m/s² * 4.0 m, solving for m gives m = 8.9 kg.

Question 17

A 500-kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0
m.
(a) What is the work done by the 5500-N force?
(b) What is the work done by gravity?
(c) What is the net work done on the elevator?

Accepted Answer

The answer of A 500-kg elevator is pulled upward with...

Question 18

A crane lifts a 425 kg steel beam vertically upward a distance of 95 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces. 
A) $3.2 \times 10 ^ { 5 } \mathrm {~J}$
B) $4.7 \times 10 ^ { 5 } \mathrm {~J}$
C) $4.0 \times 10 ^ { 5 } \mathrm {~J}$
D) $2.7 \times 10^5 \mathrm{\jmath}$

Accepted Answer

The work done by the crane can be calculated using the formula $W = Fd$, where $F$ is the force applied and $d$ is the distance moved. The force $F$ can be found by using $F = ma + mg$, where $m$ is the mass of the beam, $a$ is the acceleration, and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Substituting the given values, $F = 425 \times (1.8 + 9.8) = 425 \times 11.6 = 4930 \, \text{N}$. The work done, $W$, is then $4930 \times 95 = 468350 \, \text{J}$, which is approximately $4.7 \times 10^5 \, \text{J}$.

Question 19

A 2.0-kg object is lifted vertically through  3.00 m by a 150-N force. How much work is done on the object by gravity during this process?

Accepted Answer

The answer of A 2.0-kg object is lifted vertically through...

Question 20

A traveler pulls on a suitcase strap at an angl $36 ^ { \circ }$ above the horizontal. If 555 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?
A) 46 N
B) 52 N
C) 37 N
D) 56 N

Accepted Answer

The work done by the strap is equal to the force applied multiplied by the distance moved in the direction of the force. In this case, the distance moved in the direction of the force is the horizontal distance of 15 m. Therefore, the tension in the strap is:$$W = Fd$$$$555 J = F(15 m)$$$$F = 555 J / 15 m = 37 N$$

Quiz 6: Work and Energy

You carry a 7.0-kg bag of groceries 1.2 m above the ground at constant speed across a 2.7 m room. How much work do you do on the bag in the process?

How much work would a child do while pulling a 12-kg wagon a distance of 4.3 m with a 22 N force?

It requires 0.30 kJ of work to fully drive a stake into the ground. If the average resistive force on the stake by the ground is 828 N, how long is the stake?

An ornament of mass 40.0 g is attached to a vertical ideal spring with a force constant (spring constant) of 20.0 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?

Matthew pulls his little sister Sarah along the horizontal ground in a wagon. He exerts a force on the wagon of 60.0 N at an angle of 37.0∘37.0 ^ { \circ }37.0∘ above the horizontal. If he pulls her a distance of 12.0 m, how much work does Matthew do?

A 30-N box is pulled upward 6.0 m along the surface of a ramp that rises at 37∘37 ^ { \circ }37∘ above the horizontal. How much work does gravity do on the box during this process?

Find the net work done by friction on a box that moves in a complete circle of radius 1.82 m on a uniform horizontal floor. The coefficient of kinetic friction between the floor and the box is 0.25 , and the box weighs 65.0 N

A force of 30 N stretches a very light ideal spring 0.73 m from equilibrium. What is the force constant (spring constant) of the spring?

A very light ideal spring stretches by 21.0 cm when it is used to hang a 135-N object. What is the weight of a piece of electronic equipment that would stretch the spring by 44.9 cm if you hung the Equipment using the spring?

A person carries a 25.0-N rock through the path shown in the figure, starting at point A and ending at point B . The total time from A to B is 1.50 min. How much work did gravity do on the rock between A and B ?

A child does 350 J of work while pulling a box from the ground up to his tree house at a steady speed with a light rope. The tree house is 4.0 m above the ground. What is the mass of the box?

A 500-kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0 m. (a) What is the work done by the 5500-N force? (b) What is the work done by gravity? (c) What is the net work done on the elevator?

A crane lifts a 425 kg steel beam vertically upward a distance of 95 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

A 2.0-kg object is lifted vertically through 3.00 m by a 150-N force. How much work is done on the object by gravity during this process?

A traveler pulls on a suitcase strap at an angl 36∘36 ^ { \circ }36∘ above the horizontal. If 555 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?

Matthew pulls his little sister Sarah along the horizontal ground in a wagon. He exerts a force on the wagon of 60.0 N at an angle of $37.0 ^ { \circ }$ above the horizontal. If he pulls her a distance of 12.0 m, how much work does Matthew do?

A 30-N box is pulled upward 6.0 m along the surface of a ramp that rises at $37 ^ { \circ }$ above the horizontal. How much work does gravity do on the box during this process?

A traveler pulls on a suitcase strap at an angl $36 ^ { \circ }$ above the horizontal. If 555 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?