Question 1

A woman who weighs 700 N steps onto a scale that is in an elevator. The elevator begins to accelerate. The woman now weighs 500 N (according to the scale). The acceleration of the elevator is
A) 2.8 m/s $2$ downward.
B) 2.8 m/s $2$ upward.
C) 4.2 m/s $2$ upward.
D) 4.2 m/s $2$ downward.

Accepted Answer

The woman's apparent weight decreases, indicating the elevator accelerates downward. The difference in force (200 N) divided by her mass (700 N / 9.8 m/s$^2$) gives the acceleration magnitude, which is 2.8 m/s$^2$ downward.

Question 2

A 5.4-kg mass, placed on a smooth incline and released, begins to slide down the incline. The acceleration of the mass along the incline is 7.1 m/s $2$ . The angle of the incline (relative to the horizontal) is
A) 41°.
B) 46°.
C) 38°.
D) 36°.

Accepted Answer

The answer of A 5.4-kg mass, placed on a smooth...

Question 3

A person who weighs 1100 N steps into an elevator. The person steps onto a scale, and the elevator begins to move down to the next floor. During the movement the person has an apparent weight of 950 N. The downward acceleration of the elevator is
A) 18. m/s $2$
B) 7.5 m/s $2$
C) 14 m/s $2$
D) 1.3 m/s $2$

Accepted Answer

The apparent weight is less than the actual weight, indicating that the elevator is accelerating downwards. The apparent weight can be found using the equation $W_{apparent} = W - ma$, where $W$ is the actual weight, $m$ is the mass, and $a$ is the acceleration. Rearranging for $a$, we get $a = \frac{W - W_{apparent}}{m}$. Given $W = 1100 N$ and $W_{apparent} = 950 N$, and using $g = 9.8 m/s^2$ to find mass $m = \frac{W}{g} = \frac{1100}{9.8}$, we can solve for $a$. Plugging in the numbers, we find $a = 1.3 m/s^2$, which corresponds to choice D.

Question 4

A 13.5-N net force is applied to a stationary object. The object moves a distance of 18 m in 10 seconds. The mass of the object is
A) 15 kg.
B) 21 kg.
C) 38 kg.
D) 12 kg.

Accepted Answer

The answer of A 13.5-N net force is applied to...

Question 5

A stationary 32-kg mass has a 15-N net force applied to it. The velocity of the mass at $t = 5$ seconds is
A) 1.2 m/s.
B) 1.8 m/s.
C) 2.5 m/s.
D) 2.3 m/s.

Accepted Answer

The answer of A stationary 32-kg mass has a 15-N...

Question 6

A 21-kg mass initially at rest on a smooth table has a horizontal force applied to it. The mass moves a distance of 30 meters in 5 seconds. The magnitude of the force is
A) 50 N.
B) 64 N.
C) 71 N.
D) 79 N.

Accepted Answer

The answer of A 21-kg mass initially at rest on...

Question 7

A 13-kg mass initially at rest has a net force applied to it. The force causes the mass to reach a velocity of 12 m/s in eight seconds. The magnitude of the force is
A) 15 N.
B) 20 N.
C) 30 N.
D) 25 N.

Accepted Answer

The magnitude of the force can be found using Newton's second law, $F = ma$, where $F$ is the force, $m$ is the mass, and $a$ is the acceleration. First, find the acceleration using the formula $a = \frac{\Delta v}{\Delta t}$, where $\Delta v$ is the change in velocity and $\Delta t$ is the change in time. Here, $\Delta v = 12 \, \text{m/s}$ (final velocity) - 0 \, \text{m/s}\) (initial velocity) = $12 \, \text{m/s}$, and $\Delta t = 8 \, \text{s}$. So, $a = \frac{12 \, \text{m/s}}{8 \, \text{s}} = 1.5 \, \text{m/s}^2$. Then, using $F = ma$, $F = 13 \, \text{kg} \times 1.5 \, \text{m/s}^2 = 19.5 \, \text{N}$, which rounds to $20 \, \text{N}$, making option B correct.

Question 8

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 4-kg mass (in a direction toward the 5-kg mass). The contact force between the two masses is
A) 20 N.
B) 9 N.
C) 0 N.
D) 11 N.

Accepted Answer

The total mass is 9 kg, and the acceleration is 20 N / 9 kg = 2.22 m/s². The contact force on the 5-kg mass is 5 kg * 2.22 m/s² = 11.1 N, approximately 11 N.

Question 9

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass). The contact force between the two masses is
A) 20 N.
B) 9 N.
C) 0 N.
D) 11 N.

Accepted Answer

The answer of A 4-kg mass and a 5-kg mass...

Question 10

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass). The acceleration of the 5-kg mass is
A) 1.8 m/s $2$
B) 3.1 m/s $2$
C) 2.2 m/s $2$
D) 3.8 m/s $2$

Accepted Answer

The total mass being accelerated is 4 kg + 5 kg = 9 kg. The acceleration can be found using Newton's second law, $a = F/m$, where $F = 20$ N and $m = 9$ kg. Thus, $a = 20 \, \text{N} / 9 \, \text{kg} = 2.2 \, \text{m/s}^2$.

Question 11

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass). The acceleration of the 4-kg mass is
A) 1.8 m/s $2$
B) 3.1 m/s $2$
C) 2.2 m/s $2$
D) 3.8 m/s $2$

Accepted Answer

The total force applied is 20 N, and the total mass is 4 kg + 5 kg = 9 kg. The acceleration, a, can be found using Newton's second law, $F = ma$, giving $a = \frac{F}{m} = \frac{20}{9}$ m/s$^2$ ≈ 2.2 m/s$^2$.

Question 12

A small mass and a large mass are in contact with each other while resting on a smooth table. An external force is applied to one of the masses (in a direction toward the other mass). The contact force between the masses is
A) largest when the external force is applied to the smaller mass.
B) largest when the external force is applied to the larger mass.
C) the same whether the external force is applied to the smaller or larger mass.
D) zero in all cases.

Accepted Answer

When the external force is applied to the smaller mass, it has to accelerate both masses, requiring a larger contact force between them to accelerate the larger mass. When the force is applied to the larger mass, the required contact force to accelerate the smaller mass is less due to the smaller mass's lower inertia.

Question 13

A heavy truck is towing a small car. The mass of the truck is four times larger than the mass of the car. If the force that the truck is exerting on the car is 5000 N, the force that the car is exerting back on the truck is
A) 1300 N.
B) 20,000 N.
C) 2000 N.
D) 5000 N.

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, if the truck exerts a force of 5000 N on the car, the car exerts a force of 5000 N back on the truck, regardless of their masses.

Question 14

A small car is towing a heavy truck. The mass of the truck is four times larger than the mass of the car. If the force that the car is exerting on the truck is 2000 N, the force that the truck is exerting back on the car is
A) 1300 N.
B) 8000 N.
C) 2000 N.
D) 500 N.

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, if the car exerts a force of 2000 N on the truck, the truck exerts an equal and opposite force of 2000 N back on the car, regardless of their masses.

Question 15

A steel cable is tightly tied (horizontally) to two trees that are 8 meters apart. A 40-kg child hangs from the center of the cable-causing the center of the cable to be 1 cm below the original location (before the child grabbed the cable). The tension in the cable is
A) 78,000 N.
B) 400 N.
C) 1200 N.
D) 12,000 N.

Accepted Answer

The tension in the cable can be calculated using the formula for the tension in a horizontal cable with a weight hanging from its center, which is $T = \frac{w}{2} \times \frac{L}{d}$, where $w$ is the weight of the object hanging from the cable (in this case, the child), $L$ is the half-length of the cable, and $d$ is the displacement of the cable due to the weight. Given that the weight of the child is 40 kg (which corresponds to a force due to gravity of $w = mg = 40 \times 9.8 = 392$ N), the half-length of the cable is 4 meters (since the total length between the trees is 8 meters), and the displacement is 0.01 meters (1 cm), the tension in the cable is calculated as $T = \frac{392}{2} \times \frac{4}{0.01} = 196 \times 400 = 78,400$ N, which is approximately 78,000 N, indicating a very high tension due to the small displacement and the mechanics of the system.

Question 16

A steel cable is tightly tied (horizontally) to two trees that are 10 meters apart. A child hangs from the center of the cable, causing the center of the cable to be 2 cm below the original location (before the child grabbed the cable). The tension in the cable is 70,000 N. The mass of the child is
A) 41 kg.
B) 66 kg.
C) 57 kg.
D) 48 kg.

Accepted Answer

The tension in the cable creates a triangle with the horizontal distance and the sag. Using trigonometry and the tension, we can calculate the weight of the child. The vertical component of the tension equals the weight of the child. Solving for the child's mass gives approximately 57 kg.

Question 17

A 4-kg mass is connected to a 6-kg mass by a massless cord. A 120-N upward force is applied to the 4-kg mass, causing both masses to accelerate upward. The tension in the massless cord is
A) 60 N.
B) 48 N.
C) 40 N.
D) 72 N.

Accepted Answer

The tension in the cord can be found by considering the forces acting on the 6-kg mass as it accelerates upward. The net force on the 6-kg mass is the tension minus its weight (6kg * 9.8m/s^2). Since the system accelerates together, the net force also equals the mass of the 6-kg object times the acceleration (6kg * a). Setting these equal and solving for tension gives us the tension in the cord as 72 N.

Question 18

A 4-kg mass is connected to a 6-kg mass by a massless cord. A 120-N upward force is applied to the 4-kg mass, causing both masses to accelerate upward. The upward acceleration of the masses is
A) 12 m/s $2$
B) 2.2 m/s $2$
C) 9.8 m/s $2$
D) 5.8 m/s $2$

Accepted Answer

The total force acting on the system is the 120-N upward force minus the gravitational force acting on both masses. The gravitational force is $F_g = (4\,kg + 6\,kg) \times 9.8\,m/s^2 = 98\,N$. The net force is then $120\,N - 98\,N = 22\,N$. The total mass is $4\,kg + 6\,kg = 10\,kg$. Using Newton's second law, $F = ma$, we find the acceleration $a = \frac{F}{m} = \frac{22\,N}{10\,kg} = 2.2\,m/s^2$.

Question 19

A 6-kg mass is connected to a 4-kg mass by a massless cord. A 120-N upward force is applied to the 6-kg mass, causing both masses to accelerate upward. The tension in the massless cord is
A) 60 N.
B) 40 N.
C) 72 N.
D) 48 N.

Accepted Answer

The answer of A 6-kg mass is connected to a...

Question 20

Object A, having mass $m _ { A }$, is connected to object $\mathrm { B }$, having mass $m _ { B }$, by a massless cord. An upward force $P$ is applied to mass A, causing both masses to accelerate upward. Find the tension in the massless cord.
A) $P \times \left[ m _ { A } / \left( m _ { A } + m _ { B } \right) \right]$
B) $P \times \left[ \left( m _ { A } + m _ { B } \right) / m _ { B } \right]$
C) $P \times \left[ m _ { B } / \left( m _ { A } + m _ { B } \right) \right]$
D) $P \times \left[ \left( m _ { A } + m _ { B } \right) / m _ { A } \right]$

Accepted Answer

The tension in the cord is equivalent to the force needed to lift mass B alone, since mass A is directly acted upon by force P. This force is a fraction of P, proportional to mass B's share of the total mass, hence $P \times \left[ m _ { B } / \left( m _ { A } + m _ { B } \right) \right]$.

Quiz 5: Newtons Laws of Motion

A woman who weighs 700 N steps onto a scale that is in an elevator. The elevator begins to accelerate. The woman now weighs 500 N (according to the scale) . The acceleration of the elevator is

A 5.4-kg mass, placed on a smooth incline and released, begins to slide down the incline. The acceleration of the mass along the incline is 7.1 m/s $2$ . The angle of the incline (relative to the horizontal) is

A person who weighs 1100 N steps into an elevator. The person steps onto a scale, and the elevator begins to move down to the next floor. During the movement the person has an apparent weight of 950 N. The downward acceleration of the elevator is

A 13.5-N net force is applied to a stationary object. The object moves a distance of 18 m in 10 seconds. The mass of the object is

A stationary 32-kg mass has a 15-N net force applied to it. The velocity of the mass at $t = 5$ seconds is

A 21-kg mass initially at rest on a smooth table has a horizontal force applied to it. The mass moves a distance of 30 meters in 5 seconds. The magnitude of the force is

A 13-kg mass initially at rest has a net force applied to it. The force causes the mass to reach a velocity of 12 m/s in eight seconds. The magnitude of the force is

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 4-kg mass (in a direction toward the 5-kg mass) . The contact force between the two masses is

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass) . The contact force between the two masses is

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass) . The acceleration of the 5-kg mass is

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass) . The acceleration of the 4-kg mass is

A small mass and a large mass are in contact with each other while resting on a smooth table. An external force is applied to one of the masses (in a direction toward the other mass) . The contact force between the masses is

A heavy truck is towing a small car. The mass of the truck is four times larger than the mass of the car. If the force that the truck is exerting on the car is 5000 N, the force that the car is exerting back on the truck is

A small car is towing a heavy truck. The mass of the truck is four times larger than the mass of the car. If the force that the car is exerting on the truck is 2000 N, the force that the truck is exerting back on the car is

A steel cable is tightly tied (horizontally) to two trees that are 8 meters apart. A 40-kg child hangs from the center of the cable-causing the center of the cable to be 1 cm below the original location (before the child grabbed the cable) . The tension in the cable is

A steel cable is tightly tied (horizontally) to two trees that are 10 meters apart. A child hangs from the center of the cable, causing the center of the cable to be 2 cm below the original location (before the child grabbed the cable) . The tension in the cable is 70,000 N. The mass of the child is

A 4-kg mass is connected to a 6-kg mass by a massless cord. A 120-N upward force is applied to the 4-kg mass, causing both masses to accelerate upward. The tension in the massless cord is

A 4-kg mass is connected to a 6-kg mass by a massless cord. A 120-N upward force is applied to the 4-kg mass, causing both masses to accelerate upward. The upward acceleration of the masses is

A 6-kg mass is connected to a 4-kg mass by a massless cord. A 120-N upward force is applied to the 6-kg mass, causing both masses to accelerate upward. The tension in the massless cord is

Object A, having mass $m _ { A }$ , is connected to object $\mathrm { B }$ , having mass $m _ { B }$ , by a massless cord. An upward force $P$ is applied to mass A, causing both masses to accelerate upward. Find the tension in the massless cord.