Question 1

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the radius were changed to 1000 m, but the speed remained the same, by what factor would its centripetal acceleration change?
A)0.25
B)0.50
C)1.00
D)2.00
E)4.00

Accepted Answer

The centripetal acceleration $a_c$ is given by the formula $a_c = \frac{v^2}{r}$, where $v$ is the velocity and $r$ is the radius of the circle. If the radius $r$ is doubled (from 500 m to 1000 m) while keeping the speed $v$ constant, the new acceleration is $\frac{1}{2}$ of the original acceleration, because the radius $r$ is in the denominator. Therefore, the factor by which the centripetal acceleration changes is 0.50.

Question 2

The first of two identical boxes of mass m is sitting on level ground. The second box is sitting on a ramp that makes an angle with the ground. When a force of magnitude F is applied to each box in a direction parallel to the surface it is on, upwards on the box on the ramp, neither box moves. Which statement comparing the friction force on the box on the level, Fs,L, to the friction force on the box on the ramp, Fs,R, is correct?
A)Fs,R = Fs,L.
B)Fs,R > Fs,L.
C)Fs,R <Fs,L.
D)The coefficient of static friction is needed to determine the correct answer.
E)Depending on the values of the coefficient of static friction, the angle of elevation of the ramp, the mass of the boxes, and the applied force, answers (a), (b), and (c) are each a possible correct answer.

Accepted Answer

The correct answer is E because the coefficient of static friction, the angle of elevation of the ramp, the mass of the boxes, and the applied force all affect the friction force.

Question 3

A 1.8-kg block is released from rest at the top of a rough 30° inclined plane. As the block slides down the incline, its acceleration is 3.0 m/s² down the incline. Determine the magnitude of the force of friction acting on the block. A)4.2 N B)3.0 N C)3.4 N D)3.8 N E)2.3 N

Accepted Answer

First, we need to find the force of gravity acting on the block:
Fg = mg = (1.8 kg)(9.81 m/s^2) = 17.64 N
Next, we need to find the component of gravity that is parallel to the incline:
Fg_parallel = Fg*sin(30°) = (17.64 N)*(0.5) = 8.82 N
The force of friction is equal and opposite to the parallel component of gravity:
Ffriction = Fg_parallel = 8.82 N
Therefore, the magnitude of the force of friction acting on the block is 8.82 N, which is closest to choice C, 3.4 N.

Question 4

A small dense object is suspended from the rear view mirror in a car by a lightweight fiber. As the car is accelerating at 1.90 m/s², what angle does the string make with the vertical?

Accepted Answer

The answer of A small dense object is suspended from...

Question 5

A sample of blood is placed into a centrifuge of radius 15.0 cm. The mass of a red corpuscle is 3.0 × 10−16 kg, and the centripetal force required to make it settle out of the plasma is 4.0 × 10−11 N. At how many revolutions per second should the centrifuge be operated?

Accepted Answer

The answer of A sample of blood is placed into...

Question 6

A car enters a level, unbanked semi-circular hairpin turn of 100-m radius at a speed of 28 m/s. The coefficient of friction between the tires and the road is μ = 0.800. If the car maintains a constant speed of 28 m/s, it will
A)attempt to dig into the road surface.
B)tend to veer toward the center of the semicircle.
C)arrive safely at the end of the semicircle.
D)tend to veer toward the outside of the circle.
E)veer toward the center for the first quarter-circle, then veer toward the outside for the second quarter-circle.

Accepted Answer

The car will arrive safely at the end of the semicircle if the centripetal force acting on the car is less than or equal to the maximum frictional force that the tires can provide.

Centripetal force = (mass of car) x (centripetal acceleration) 
Centripetal acceleration = (velocity)^2 / (radius) 
Max frictional force = (coefficient of friction) x (normal force)

Assuming a flat road surface and level turn, the normal force is equal to the weight of the car. 
Max frictional force = (0.8) x (weight of car)

Now, we can compare the centripetal force and the max frictional force: 
Centripetal force = (mass of car) x (centripetal acceleration) 
Centripetal force = (mass of car) x [(velocity)^2 / (radius)] 
Centripetal force = (mass of car) x (28 m/s)^2 / (100 m) 
Centripetal force = (mass of car) x 7.84 m/s^2

Now let's compare the centripetal force and the max frictional force: 
Centripetal force <= max frictional force 
(mass of car) x 7.84 m/s^2 <= (0.8) x (weight of car)

We can simplify this to: 
mass of car <= 0.102 x weight of car

Since the mass of the car is a fixed value, the weight of the car cannot exceed a certain limit in order for the car to make the turn safely. Based on the given information, we cannot determine the weight of the car or whether it falls under this limit. However, we can say with certainty that the car will arrive safely at the end of the semicircle as long as the weight of the car is within the safe limit.

Question 7

The following equation was obtained by solving a physics problem:  The best physical representation of the situation is
A)A car traveling at 16.0 m/s is 19.2° into a turn of a quarter circle on a level road.
B)A mass on a string that is originally horizontal has fallen to where the angle between the string and the vertical direction is 19.2°.
C)A mass on a string originally horizontal has fallen 19.2° from the horizontal direction.
D)A car traveling at 16.0 m/s is on a circular curve banked at 19.2°.
E)A car traveling at 16.0 m/s and going over a semicircular mountain-top road is 19.2° down from the top.

Accepted Answer

The equation obtained from the physics problem involves centripetal force and the banked angle of a circular curve. Therefore, the best representation of the situation is a car traveling at a constant speed of 16.0 m/s on a circular curve that is banked at an angle of 19.2°.

Question 8

A 1.8-kg block is projected up a rough 10° inclined plane. As the block slides up the incline, its acceleration is 3.8 m/s² down the incline. What is the magnitude of the force of friction acting on the block? A)5.0 N B)3.8 N C)4.2 N D)4.6 N E)6.5 N

Accepted Answer

The answer of A 1.8-kg block is projected up a...

Question 9

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 500-m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change?
A)0.25
B)0.50
C)1.00
D)2.00
E)4.00

Accepted Answer

The centripetal acceleration $a_c$ is given by the formula $a_c = \frac{v^2}{r}$, where $v$ is the velocity and $r$ is the radius of the circle. When the speed doubles from 150 m/s to 300 m/s, the square of the speed ($v^2$) increases by a factor of $4$ ($(300/150)^2 = 2^2 = 4$), hence the centripetal acceleration increases by a factor of $4$.

Question 10

A car enters a level, unbanked semi-circular hairpin turn of 300 m radius at a speed of 40 m/s. The coefficient of friction between the tires and the road is μ = 0.25. If the car maintains a constant speed of 40 m/s, it will
A)attempt to dig into the road surface.
B)tend to veer toward the center of the semicircle.
C)arrive safely at the end of the semicircle.
D)tend to veer toward the outside of the circle.
E)veer toward the center for the first quarter-circle, then veer toward the outside for the second quarter-circle.

Accepted Answer

The car will tend to veer toward the outside of the circle due to the centripetal force acting on it. The centripetal force required to keep the car moving in a circular path at 40 m/s is Fc = mv^2/r = (1000 kg)(40 m/s)^2/300 m = 5333.33 N. The maximum friction force that can be exerted on the car is μN = μmg = (0.25)(1000 kg)(9.8 m/s^2) = 2450 N. This is less than the required centripetal force, so the car will begin to slide toward the outside of the turn.

Question 11

What is the net force on a 10-kg solid steel sphere falling in air at terminal speed?
A)980 N
B)200 N
C)98 N
D)49 N
E)Some value other than those given above.

Accepted Answer

At terminal speed, the net force on an object is zero because the force of gravity is balanced by the drag force.

Question 12

If a dense 20.0-kg object is falling in air at half its terminal velocity, what is the drag force on the object at this moment?
A)24.5 N
B)49.0 N
C)69.3 N
D)98.0 N
E)139 N

Accepted Answer

When the object is falling at half its terminal velocity, its acceleration is half of the acceleration due to gravity (9.8 m/s²). Thus, its acceleration is 4.9 m/s². At this point, the net force on the object is equal to the gravitational force on the object minus the drag force on the object. Using Newton's second law, we can write:

Fnet = ma
mg - Fdrag = ma
Fdrag = mg - ma

Substituting the given values, we get:

Fdrag = (20.0 kg)(9.8 m/s²) - (20.0 kg)(4.9 m/s²) = 98.0 N - 49.0 N = 49.0 N

Therefore, the drag force on the object at this moment is 49.0 N.

Question 13

A 2.0-kg block slides on a rough horizontal surface. A force (P = 6.0 N) is applied to the block as shown. The magnitude of the block's acceleration is 1.2 m/s². What is the magnitude of the force of friction acting on the block? A)2.0 N B)1.4 N C)1.6 N D)2.8 N E)3.4 N

Accepted Answer

The answer of A 2.0-kg block slides on a rough...

Question 14

An airplane pilot experiences weightlessness as she passes over the top of a loop-the-loop maneuver. If her speed is 200 m/s at the time, find the radius of the loop.

Accepted Answer

The answer of An airplane pilot experiences weightlessness as she...

Question 15

A skydiver of 75-kg mass has a terminal velocity of 60 m/s. At what speed is the resistive force on the skydiver half that when at terminal speed?
A)15 m/s
B)49 m/s
C)30 m/s
D)42 m/s
E)36 m/s

Accepted Answer

The answer of A skydiver of 75-kg mass has a...

Question 16

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 1000-m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change?
A)0.25
B)0.50
C)1.00
D)2.00
E)4.00

Accepted Answer

We know that the centripetal acceleration of an object moving in a circle is given by:

a = v^2/r

where v is the speed of the object and r is the radius of the circle.

In the first case, the airplane is moving at a speed of 150 m/s and a radius of 500 m. Therefore, its centripetal acceleration is:

a1 = (150 m/s)^2 / 500 m = 45 m/s^2

In the second case, the airplane is moving at a speed of 300 m/s and a radius of 1000 m. Therefore, its centripetal acceleration is:

a2 = (300 m/s)^2 / 1000 m = 90 m/s^2

To find the factor by which the centripetal acceleration changes, we can simply divide a2 by a1:

a2/a1 = 90 m/s^2 / 45 m/s^2 = 2

Therefore, the centripetal acceleration changes by a factor of 2 when the speed of the airplane is doubled while flying in the same circle.

Question 17

A space station in the form of a large wheel, 120 m in diameter, rotates to provide an "artificial gravity" of 3.00 m/s² for persons located at the outer rim. Find the rotational frequency of the wheel (in revolutions per minute) that will produce this effect.

Accepted Answer

The answer of A space station in the form of...

Question 18

If a 20-kg object dropped in air has a terminal speed of 60 m/s, what was its acceleration at 30 m/s? A)9.80 m/s² B)7.35 m/s² C)4.90 m/s² D)2.45 m/s² E)More information is needed to answer this question.

Accepted Answer

The answer of If a 20-kg object dropped in air...

Question 19

A race car starts from rest on a circular track of radius 400 m. Its speed increases at the constant rate of 0.500 m/s². At the point where the magnitudes of the radial and tangential accelerations are equal, determine (a) the speed of the race car, and (b) the elapsed time.

Accepted Answer

The answer of A race car starts from rest on...

Question 20

A 3.0-kg block slides on a rough horizontal surface. A force of 8.0 N acting parallel to the surface is applied to the block. The coefficient of kinetic friction between the block and the surface is 0.15. What is the magnitude of the block's acceleration? A)1.9 m/s² B)1.2 m/s² C)2.3 m/s² D)1.5 m/s² E)2.9 m/s²

Accepted Answer

The answer of A 3.0-kg block slides on a rough...

Quiz 6: Applications of Newtons Laws of Motion

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the radius were changed to 1000 m, but the speed remained the same, by what factor would its centripetal acceleration change?

A 1.8-kg block is released from rest at the top of a rough 30° inclined plane. As the block slides down the incline, its acceleration is 3.0 m/s2 down the incline. Determine the magnitude of the force of friction acting on the block.

A small dense object is suspended from the rear view mirror in a car by a lightweight fiber. As the car is accelerating at 1.90 m/s2, what angle does the string make with the vertical?

A sample of blood is placed into a centrifuge of radius 15.0 cm. The mass of a red corpuscle is 3.0 × 10−16 kg, and the centripetal force required to make it settle out of the plasma is 4.0 × 10−11 N. At how many revolutions per second should the centrifuge be operated?

A car enters a level, unbanked semi-circular hairpin turn of 100-m radius at a speed of 28 m/s. The coefficient of friction between the tires and the road is μ = 0.800. If the car maintains a constant speed of 28 m/s, it will

The following equation was obtained by solving a physics problem: The best physical representation of the situation is

A 1.8-kg block is projected up a rough 10° inclined plane. As the block slides up the incline, its acceleration is 3.8 m/s2 down the incline. What is the magnitude of the force of friction acting on the block?

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 500-m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change?

A car enters a level, unbanked semi-circular hairpin turn of 300 m radius at a speed of 40 m/s. The coefficient of friction between the tires and the road is μ = 0.25. If the car maintains a constant speed of 40 m/s, it will

What is the net force on a 10-kg solid steel sphere falling in air at terminal speed?

If a dense 20.0-kg object is falling in air at half its terminal velocity, what is the drag force on the object at this moment?

A 2.0-kg block slides on a rough horizontal surface. A force (P = 6.0 N) is applied to the block as shown. The magnitude of the block's acceleration is 1.2 m/s2. What is the magnitude of the force of friction acting on the block?

An airplane pilot experiences weightlessness as she passes over the top of a loop-the-loop maneuver. If her speed is 200 m/s at the time, find the radius of the loop.

A skydiver of 75-kg mass has a terminal velocity of 60 m/s. At what speed is the resistive force on the skydiver half that when at terminal speed?

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 1000-m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change?

A space station in the form of a large wheel, 120 m in diameter, rotates to provide an "artificial gravity" of 3.00 m/s2 for persons located at the outer rim. Find the rotational frequency of the wheel (in revolutions per minute) that will produce this effect.

If a 20-kg object dropped in air has a terminal speed of 60 m/s, what was its acceleration at 30 m/s?

A race car starts from rest on a circular track of radius 400 m. Its speed increases at the constant rate of 0.500 m/s2. At the point where the magnitudes of the radial and tangential accelerations are equal, determine (a) the speed of the race car, and (b) the elapsed time.

A 3.0-kg block slides on a rough horizontal surface. A force of 8.0 N acting parallel to the surface is applied to the block. The coefficient of kinetic friction between the block and the surface is 0.15. What is the magnitude of the block's acceleration?

A 1.8-kg block is released from rest at the top of a rough 30° inclined plane. As the block slides down the incline, its acceleration is 3.0 m/s² down the incline. Determine the magnitude of the force of friction acting on the block.

A small dense object is suspended from the rear view mirror in a car by a lightweight fiber. As the car is accelerating at 1.90 m/s², what angle does the string make with the vertical?

A 1.8-kg block is projected up a rough 10° inclined plane. As the block slides up the incline, its acceleration is 3.8 m/s² down the incline. What is the magnitude of the force of friction acting on the block?

A 2.0-kg block slides on a rough horizontal surface. A force (P = 6.0 N) is applied to the block as shown. The magnitude of the block's acceleration is 1.2 m/s². What is the magnitude of the force of friction acting on the block?

A space station in the form of a large wheel, 120 m in diameter, rotates to provide an "artificial gravity" of 3.00 m/s² for persons located at the outer rim. Find the rotational frequency of the wheel (in revolutions per minute) that will produce this effect.

A race car starts from rest on a circular track of radius 400 m. Its speed increases at the constant rate of 0.500 m/s². At the point where the magnitudes of the radial and tangential accelerations are equal, determine (a) the speed of the race car, and (b) the elapsed time.