Question 1

A car goes around a circular curve on a horizontal road at constant speed. What is the direction of the friction force on the car due to the road?
A) perpendicular to the curve outward
B) tangent to the curve in the forward direction
C) tangent to the curve opposite to the direction of the car's motion
D) perpendicular to the curve inward
E) There is no friction on the car because its speed is constant.

Accepted Answer

The friction force acts perpendicular to the curve inward, providing the centripetal force necessary for the car to turn around the curve. This force is what keeps the car from sliding outward due to its inertia.

Question 2

When an object moves in uniform circular motion, the direction of its acceleration is
A) in the same direction as its velocity vector.
B) depends on the speed of the object.
C) in the opposite direction of its velocity vector.
D) is directed toward the center of its circular path.
E) is directed away from the center of its circular path.

Accepted Answer

In uniform circular motion, the acceleration is always directed toward the center of the circle. This is known as centripetal acceleration, which is necessary to change the direction of the velocity vector, keeping the object moving in a circular path.

Question 3

Planet A has twice the mass of Planet B. From this information, what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B?
A) The acceleration due to gravity on Planet A is greater than the acceleration due to gravity on Planet B, but we cannot say how much greater.
B) The acceleration due to gravity on Planet A must be four times as great as the acceleration due to gravity on Planet B.
C) The acceleration due to gravity on Planet A is the same as the acceleration due to gravity on Planet B.
D) The acceleration due to gravity on Planet A must be twice as great as the acceleration due to gravity on Planet B.
E) We cannot conclude anything about the acceleration due to gravity on Planet A without knowing the radii of the two planets.

Accepted Answer

The acceleration due to gravity is determined not only by the mass of a planet but also by its radius. Without knowing the radii of the planets, we cannot accurately compare the gravitational accelerations.

Question 4

When a car goes around a banked circular curve at the proper speed speed for the banking angle, what force cause it to follow the circular path?
A) the friction force from the road
B) the normal force from the road
C) gravity
D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration.

Accepted Answer

The normal force from the road is responsible for providing the centripetal force necessary for the car to follow the circular path when it is traveling at the proper speed for the banking angle. This is because the normal force can be resolved into components, one of which points towards the center of the circular path, acting as the centripetal force.

Question 5

A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to
Gravity at the surface of the earth?
A) g/8
B) g/16
C) g
D) g/4
E) g/2

Accepted Answer

The acceleration due to gravity (g) is given by the formula $g = \frac{G M}{R^2}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, and $R$ is the radius of the planet. If the mass of the hypothetical planet is half that of Earth ($M/2$) and its radius is twice that of Earth ($2R$), the acceleration due to gravity on the planet would be $g' = \frac{G (M/2)}{(2R)^2} = \frac{G M}{4R^2} \cdot \frac{1}{2} = \frac{g}{8}$, where $g = \frac{G M}{R^2}$ is the acceleration due to gravity on Earth.

Question 6

Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely
To slide on the pavement as it goes around the curve?
A) the car with the new tires
B) Neither car will slide.
C) the car with the bald tires
D) It depends on if the pavement is wet or dry.

Accepted Answer

When cars go around a banked curve at the proper speed for the banking angle, the force necessary to keep them in their circular path is provided by the normal force from the banking of the road, not by friction. Therefore, both cars with excellent traction and bald tires will not slide if they are traveling at the correct speed for the banking angle.

Question 7

If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does
not spill out. This happens because an outward force balances the pull of gravity on the water.

Accepted Answer

At the highest point, the water does not spill out due to the centripetal force acting towards the center of the circle, which is provided by the tension in the bucket handle and the gravitational force acting on the water, not an outward force.

Question 8

If you stood on a planet having a mass four times that of Earth's mass, and a radius two times that of Earth's radius, you would weigh
A) two times less than you do on Earth.
B) two times more than you do on Earth.
C) the same as you do on Earth.
D) four times more than you do on Earth.

Accepted Answer

The gravitational force is proportional to the mass of the planet and inversely proportional to the square of the radius. If the mass is four times greater and the radius is two times greater, the gravitational force (and thus your weight) would be (4/(2^2)) = 1, meaning you would weigh the same as on Earth.

Question 9

Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is
Changed to 4r. What is the magnitude of the new gravitational force? 
A)  16F 
B)  4F 
C)  F/16 
D)  F/4 
E)  F/2

Accepted Answer

The gravitational force between two masses is given by $F = G\frac{mM}{r^2}$, where $G$ is the gravitational constant, $m$ and $M$ are the masses of the two objects, and $r$ is the distance between their centers. When the masses are changed to $2m$ and $2M$, and the distance is changed to $4r$, the new force $F'$ can be calculated as $F' = G\frac{(2m)(2M)}{(4r)^2}$. Simplifying this gives $F' = G\frac{4mM}{16r^2} = \frac{1}{4}G\frac{mM}{r^2} = \frac{1}{4}F$, so the magnitude of the new gravitational force is $F/4$.

Question 10

Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B? 
A)  m/4 
B) $\mathrm { m } / \sqrt { 2 }$
C)  4m 
D)  m 
E) $m \sqrt { 2 }$

Accepted Answer

The surface gravity $g$ is given by $g = \frac{Gm}{r^2}$, where $G$ is the gravitational constant, $m$ is the mass of the planet, and $r$ is the radius of the planet. If planet B has twice the radius of planet A, its radius is $2r$. For the surface gravity to be the same on both planets, the mass of planet B must be such that the increase in radius (which would decrease the gravity) is offset by an increase in mass. Setting the gravities equal gives $\frac{Gm}{r^2} = \frac{Gm_B}{(2r)^2}$, solving for $m_B$ gives $m_B = 4m$, indicating that planet B must have four times the mass of planet A to have the same surface gravity.

Question 11

An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is
A) zero.
B) one-third of its weight on the surface of the earth.
C) the same as on the surface of the earth.
D) one-quarter of its weight on the surface of the earth.
E) one-half of its weight on the surface of the earth.

Accepted Answer

The gravitational force (weight) decreases with the square of the distance from the center of the Earth. At two Earth radii, the distance is doubled, so the weight is (1/2)^2 = 1/4 of its weight on the surface.

Question 12

Two small objects, with masses m and M, are originally a distance r apart, and the gravitational force on each one has magnitude F. The second object has its mass changed to 2M, and the
Distance is changed to r/4. What is the magnitude of the new gravitational force?
A) 16F
B) 32F
C) F/16
D) F/32
E) 2F

Accepted Answer

The gravitational force between two masses is given by $F = G\frac{mM}{r^2}$, where $G$ is the gravitational constant, $m$ and $M$ are the masses, and $r$ is the distance between the centers of the two masses. When the mass of the second object is doubled to $2M$ and the distance is reduced to $r/4$, the new force $F'$ can be calculated as $F' = G\frac{m(2M)}{(r/4)^2} = G\frac{2mM}{r^2/16} = 16G\frac{mM}{r^2}$, which is $16$ times the original force $F$.

Question 13

The acceleration due to gravity on Planet A is one-sixth what it is on Planet B, and the radius of the Planet A is one-fourth that of Planet B. The mass of Planet A is what fraction of the mass of
Planet B?
A) 1/24
B) 1/16
C) 1/6
D) 1/12
E) 1/96

Accepted Answer

The answer of The acceleration due to gravity on Planet...

Question 14

A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity?
A) when it is closer to the Moon than it is to Earth
B) when it is half-way there
C) when it gets above the atmosphere
D) It is never beyond the pull of Earth's gravity.

Accepted Answer

Earth's gravity extends into space and never truly ends, but its strength decreases with distance. Therefore, a spaceship traveling to the Moon remains within Earth's gravitational influence, although the Moon's gravity becomes more significant as the spacecraft approaches it.

Question 15

You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the
Ice, it
A) moves along a straight-line path away from the center of the circle.
B) moves along a straight-line path toward the center of the circle.
C) continues to follow a circular path, but with a radius larger than the original radius.
D) moves along a path that is neither straight nor circular.
E) moves along a straight-line path in its original direction.

Accepted Answer

When the force of friction between the tires and the road becomes zero, the car can no longer follow the circular path because there is no centripetal force to keep it moving in a circle. According to Newton's first law of motion, an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Since the frictional force has disappeared, there's no force to change the car's direction, so it will continue moving in a straight line in the direction it was going at the moment it hit the ice.

Question 16

Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B?
A)  2r 
B)  r 
C) $r \sqrt { 2 }$
D)  4r 
E) $r / \sqrt { 2 }$

Accepted Answer

Surface gravity $g = \frac{Gm}{r^2}$, where $G$ is the gravitational constant, $m$ is the mass, and $r$ is the radius. If planet B has twice the mass of planet A ($2m$) and the same surface gravity, then $r_B = r_A \sqrt{2}$ to keep $g$ constant, because the radius must increase by the square root of the mass increase to maintain the same $g$.

Question 17

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If gm is the acceleration due to gravity at the surface of Mars, what is the acceleration due to gravity at the
Location of the satellite?
A) gm/9
B) gm
C) 0
D) gm/16
E) gm/3

Accepted Answer

The answer of A satellite encircles Mars at a distance...

Question 18

The reason an astronaut in an earth satellite feels weightless is that
A) the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel.
B) this is a psychological effect associated with rapid motion.
C) the astronaut is falling.
D) the astronaut is beyond the range of the earth's gravity.
E) the astronaut's acceleration is zero.

Accepted Answer

The astronaut feels weightless because they are in a state of free fall towards Earth. The satellite, along with the astronaut inside it, is continuously falling towards Earth but also moving forward, so it keeps missing the Earth. This creates the sensation of weightlessness.

Question 19

Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the
Attractive force on each one? 
A)  F 
B)  16 F 
C)  F/4
D)  4 F 
E)  8 F

Accepted Answer

Doubling both masses increases the force by a factor of 4 (since gravitational force is proportional to the product of the masses), but doubling the separation decreases the force by a factor of 4 (since gravitational force is inversely proportional to the square of the separation distance). These changes cancel out, leaving the force unchanged at F.

Question 20

When a car goes around a circular curve on a horizontal road at constant speed, what force causes it to follow the circular path?
A) gravity
B) the friction force from the road
C) the normal force from the road
D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration.

Accepted Answer

The friction force from the road provides the centripetal force necessary for the car to follow a circular path. Even though the car is moving at a constant speed, it is still accelerating due to the change in direction, and this acceleration is provided by the frictional force.

Quiz 5: Circular Motion; Gravitation

A car goes around a circular curve on a horizontal road at constant speed. What is the direction of the friction force on the car due to the road?

When an object moves in uniform circular motion, the direction of its acceleration is

Planet A has twice the mass of Planet B. From this information, what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B?

When a car goes around a banked circular curve at the proper speed speed for the banking angle, what force cause it to follow the circular path?

A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to Gravity at the surface of the earth?

Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely To slide on the pavement as it goes around the curve?

If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens because an outward force balances the pull of gravity on the water.

If you stood on a planet having a mass four times that of Earth's mass, and a radius two times that of Earth's radius, you would weigh

Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is Changed to 4r. What is the magnitude of the new gravitational force?

Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B?

An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is

Two small objects, with masses m and M, are originally a distance r apart, and the gravitational force on each one has magnitude F. The second object has its mass changed to 2M, and the Distance is changed to r/4. What is the magnitude of the new gravitational force?

The acceleration due to gravity on Planet A is one-sixth what it is on Planet B, and the radius of the Planet A is one-fourth that of Planet B. The mass of Planet A is what fraction of the mass of Planet B?

A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity?

You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the Ice, it

Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B?

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If gm is the acceleration due to gravity at the surface of Mars, what is the acceleration due to gravity at the Location of the satellite?

The reason an astronaut in an earth satellite feels weightless is that

Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the Attractive force on each one?

When a car goes around a circular curve on a horizontal road at constant speed, what force causes it to follow the circular path?