Question 1

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)the normal force from the road
B)the friction 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 force that causes the car to follow the circular path is the friction force from the road. This force acts inward toward the center of the curve and is necessary to provide the centripetal acceleration required to keep the car moving in a circular path. The normal force from the road is perpendicular to the surface of the road and does not directly cause the car to follow the circular path. Gravity also does not directly cause the car to follow the circular path, although it does affect the weight of the car and the friction force. Choice D is incorrect because the car may be traveling at a constant speed, but it is still undergoing acceleration due to the change in direction.

Question 2

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

Accepted Answer

It is never beyond the pull of Earth's gravity. Gravity is a force that extends infinitely and decreases with distance. Even when the spaceship reaches the Moon, it is still within the gravitational field of Earth. However, the gravitational force of the Moon may be greater than that of Earth at the point nearest to it, which is called the "Lunar Gravity Well."

Question 3

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/ $\sqrt { 2 }$
B)m
C)m $\sqrt { 2 }$
D)4m
E)m/4

Accepted Answer

The surface gravity $ g $ is given by $ g = \frac{Gm}{r^2} $. Since both planets have the same surface gravity, $ \frac{Gm_A}{r_A^2} = \frac{Gm_B}{r_B^2} $. Given $ r_B = 2r_A $, substituting gives $ \frac{m}{r_A^2} = \frac{m_B}{(2r_A)^2} $. Solving for $ m_B $ gives $ m_B = 4m $.

Question 4

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 must be twice as great as the acceleration due to gravity on Planet B.
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 is greater than the acceleration due to gravity on Planet B, but we cannot say how much greater.
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 two planets, we cannot accurately compare the accelerations due to gravity on their surfaces.

Question 5

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If g_m 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)g_m/9 B)0 C)g_m D)g_m/3 E)g_m/16

Accepted Answer

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

Question 6

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)F/32
B)F/16
C)16F
D)32F
E)2F

Accepted Answer

The answer of Two small objects, with masses m and...

Question 7

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)the car with the bald tires
C)Neither car will slide.
D)It depends on if the pavement is wet or dry.

Accepted Answer

The answer of Two cars go around a banked curve...

Question 8

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 normal force from the road
B)the friction 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 directed perpendicular to the surface of the road and acts to balance the weight of the car. When the road is banked at the proper angle, the normal force also has a horizontal component that acts towards the center of the circular path. This horizontal component, along with the car's inertia, causes it to follow the circular path without any need for additional forces such as friction or gravity.

Question 9

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

Accepted Answer

In uniform circular motion, the direction of the acceleration is always directed toward the center of the circular path. This is because the velocity vector of the object is constantly changing direction, even though its speed is constant. Mathematically, this is expressed as a = v^2/r, where a is the acceleration, v is the speed, and r is the radius of the circular path. This equation shows that the acceleration is directly proportional to the square of the speed and inversely proportional to the radius, but always directed toward the center of the path.

Question 10

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)r/ $\sqrt { 2 }$
B)r
C)r $\sqrt { 2 }$
D)4r
E)2r

Accepted Answer

The surface gravity $ g $ is given by $ g = \frac{GM}{r^2} $. Since both planets have the same surface gravity, $ \frac{GM_A}{r_A^2} = \frac{GM_B}{r_B^2} $. Given $ M_B = 2M_A $ and $ r_A = r $, solving for $ r_B $ gives $ r_B = r \sqrt{2} $.

Question 11

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)tangent to the curve in the forward direction
B)tangent to the curve opposite to the direction of the car's motion
C)perpendicular to the curve outward
D)perpendicular to the curve inward
E)There is no friction on the car because its speed is constant.

Accepted Answer

The friction force on the car due to the road will be perpendicular to the curve inward, towards the center of the circle, because it is providing the centripetal force required to keep the car moving in a circular path. This friction force acts inwards so that the car doesn't slide off the road in the outward direction.

Question 12

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)the same as you do on Earth.
B)two times more than you do on Earth.
C)two times less than you do on Earth.
D)four times more than you do on Earth.

Accepted Answer

The gravitational force that you feel (which translates to your weight) depends on both the mass of the planet and the distance from its center (radius). The formula for gravitational force is $F = G \frac{m_1 m_2}{r^2}$, where $m_1$ and $m_2$ are the masses involved, $r$ is the distance between their centers, and $G$ is the gravitational constant. If the mass of the planet is four times that of Earth and the radius is two times that of Earth, the increase in mass would tend to make you weigh four times more, but the increase in radius would square in the denominator, making the gravitational pull four times weaker (since $2^2 = 4$). These effects cancel each other out, so you would weigh the same as you do on Earth.

Question 13

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
B)g/2
C)g/4
D)g/8
E)g/16

Accepted Answer

The acceleration due to gravity on a planet is given by the formula: 
g = G M/R^2 
where G is the universal gravitational constant, M is the mass of the planet, and R is its radius. 
Comparing the planet with Earth: 
Mass of the planet, M = (1/2) Mass of Earth, Me 
Radius of the planet, R = 2 Radius of Earth, Re 
Putting the values in the formula: 
g = G (1/2) Me / (2Re)^2 
g = G Me / (2^2 x Re^2 x 2) 
g = G Me / (8 x Re^2) 
g = (1/8) G Me / Re^2 
g/8 = G M/R^2 
Therefore, the acceleration due to gravity on the planet is g/8 or (D).

Question 14

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 15

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

Accepted Answer

The reason an astronaut in an earth satellite feels weightless is that they are falling towards the Earth due to gravity, but their velocity is such that they are also moving horizontally fast enough to never hit the Earth. This continuous state of free fall gives the sensation of weightlessness.

Question 16

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)the same as on the surface of the earth.
C)one-half of its weight on the surface of the earth.
D)one-third of its weight on the surface of the earth.
E)one-quarter 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 from the center, the distance is doubled, so the weight is (1/2)^2 = 1/4 of its weight on the surface of the Earth.

Question 17

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)F/16
B)F/4
C)16F
D)4F
E)F/2

Accepted Answer

The answer of Two small objects, with masses m and...

Question 18

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)1/6
B)1/16
C)1/24
D)1/96
E)1/12

Accepted Answer

Let's assume the mass of Planet A is $m_A$ and the mass of Planet B is $m_B$.

We know that the acceleration due to gravity on Planet A, $g_A$, is $\frac{1}{6}$ times the acceleration due to gravity on Planet B, $g_B$. Mathematically, we can write:

$$ g_A = \frac{1}{6} g_B $$

We also know that the radius of Planet A, $r_A$, is $\frac{1}{4}$ times the radius of Planet B, $r_B$. Mathematically, we can write:

$$ r_A = \frac{1}{4} r_B $$

We can use the formula for acceleration due to gravity on a planet, which is:

$$ g = \frac{Gm}{r^2} $$

where $G$ is the gravitational constant, $m$ is the mass of the planet, and $r$ is the radius of the planet.

Using this formula for Planet A and B, we can write:

$$ g_A = \frac{Gm_A}{r_A^2} $$

and

$$ g_B = \frac{Gm_B}{r_B^2} $$

We can substitute the values we know for $g_A$, $g_B$, $r_A$, and $r_B$ into these equations and simplify:

$$ \frac{Gm_A}{(\frac{1}{4}r_B)^2} = \frac{1}{6} \frac{Gm_B}{r_B^2} $$

Simplifying this equation, we get:

$$ m_A = \frac{1}{96} m_B $$

Therefore, the mass of Planet A is $\frac{1}{96}$ times the mass of Planet B, which is answer choice D).

Question 19

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)moves along a straight-line path in its original direction.
D)continues to follow a circular path, but with a radius larger than the original radius.
E)moves along a path that is neither straight nor circular.

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 in a straight line unless acted upon by an external force. Therefore, the car will move along a straight-line path in its original direction at the point where it hit the ice.

Question 20

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)16F
B)8F
C)4F
D)F
E)F/4

Accepted Answer

The gravitational force between two masses is given by $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the separation between the centers of the two masses. If both masses are doubled ($2m_1$ and $2m_2$) and the separation is also doubled ($2r$), the new force $F'$ can be calculated as $F' = G\frac{(2m_1)(2m_2)}{(2r)^2}$. Simplifying this gives $F' = G\frac{4m_1m_2}{4r^2} = G\frac{m_1m_2}{r^2} = F$, meaning the force remains the same.

Quiz 6: Gravity

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

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?

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 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?

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?

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?

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?

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

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 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?

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 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?

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.

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

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 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?

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?

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