Question 1

If the diameter of the Earth were suddenly reduced to one-fourth of its present size while its mass remained the same,how would your weight be altered?

Accepted Answer

Weight is directly proportional to the mass and inversely proportional to the square of the distance between two objects.

If the diameter of the Earth is reduced to one-fourth of its present size while the mass remains the same, the distance between the center of the Earth and the surface (where we stand) would be reduced to one-half of its initial value.

Therefore, the weight would increase by a factor of (1/2)^2 = 1/4.

However, since the mass remains the same, the weight would increase by a factor of 4.

So, the weight would be 16 times as great as before.

Question 2

A hockey puck is seen moving north over a frozen pond at a speed of 2m/sec.A while later it is seen moving west at 2m/sec.Which of the following correctly describes the forces acting on the puck?

Accepted Answer

Since the direction of motion of the hockey puck has changed, it means that a force has acted on it. The force must have been applied in a direction perpendicular to the initial direction of motion, in this case, in a westward direction, to cause it to move towards the west. Therefore, choice A is correct. Choice B is incorrect because the direction of motion has changed, even though the speed remains the same. Choice C is incorrect because the force must have been applied in a westward direction, not a northward direction. Choice D is incorrect because we can conclude that a force has acted from the given information.

Question 3

What happens to the angular momentum of a planet as it orbits the Sun?

Accepted Answer

According to the conservation of angular momentum, the angular momentum of a planet remains constant as it orbits the Sun. This means that the product of its moment of inertia and angular velocity stays constant. As the planet gets closer to the Sun, it speeds up, and when it moves away, it slows down, but its angular momentum remains the same.

Question 4

For an object to accelerate it must change its

Accepted Answer

Acceleration is defined as a change in the velocity of an object, which can occur through a change in its speed, its direction of motion, or both.

Question 5

Suppose an astronaut whose mass is 50 kg pushes herself away from an artificial satellite that has a mass of 500 kg.While she is pushing,the acceleration of the satellite is 1 m/s per second.What is the acceleration of the astronaut?

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the astronaut pushes against the satellite, both experience forces of equal magnitude but in opposite directions. The acceleration of an object is given by the formula $a = \frac{F}{m}$, where $a$ is the acceleration, $F$ is the force applied, and $m$ is the mass of the object. Since the force exerted by the astronaut on the satellite is the same as the force exerted by the satellite on the astronaut, but the astronaut's mass is 1/10th that of the satellite, her acceleration will be 10 times greater than that of the satellite. Therefore, if the satellite's acceleration is 1 m/s^2, the astronaut's acceleration will be 10 m/s^2.

Question 6

A mass of 50 kg is acted on by a force of 200 N.The motion of the object subsequently will be

Accepted Answer

To determine the motion of an object, we need to use Newton's second law: F = ma (where F is the force, m is the mass, and a is the acceleration). 
In this case, F = 200 N and m = 50 kg. Plugging these values into the equation, we get: 
200 = 50a 
Solving for a, we get: 
a = 4 m/sec^2 
Therefore, the object will accelerate at a rate of 4 m/sec^2.

Question 7

How will an object move if there are no forces acting on it?

Accepted Answer

According to Newton's first law of motion, an object at rest or in motion will remain in that state unless a force acts upon it. Therefore, if there are no forces acting on an object, it will continue to move in a straight line at a constant speed. This is also known as uniform motion.

Question 8

Which of the following bodies is accelerating?

Accepted Answer

A body moving in a circle at constant speed is constantly changing its direction, thus experiencing acceleration even though its speed may be constant. The other choices do not experience acceleration.

Question 9

The force required to keep an object in a circular orbit is directed

Accepted Answer

The force required to keep an object in a circular orbit is called centripetal force. Centripetal force is always directed towards the center of the circle, as it is responsible for changing the direction of the object's motion, keeping it constantly in a circular path. Therefore, the correct choice is D - Toward the center of the circle.

Question 10

Suppose an object moves in a circular path at constant speed.What can be said about the force acting on it?

Accepted Answer

The object moving in a circular path at constant speed experiences a force called centripetal force, which is always directed towards the center of the circle. Therefore, the force acting on it must vary in direction to keep the object moving in a circular path.

Question 11

What is always true when an object accelerates?

Accepted Answer

According to Newton's Second Law, an object accelerates when a net force acts upon it. Therefore, it is always true that a force is acting on an object when it accelerates. Option A is not always true as an object can also decelerate. Option B is not always true as an object can accelerate in a straight line. Option D is not true as an object's mass is constant, unless some external factor changes it.

Question 12

If the distance between two objects is doubled,the force of gravity they exert on each other will

Accepted Answer

According to Newton's Law of Universal Gravitation, the force of gravity between two objects is inversely proportional to the square of the distance between them. Therefore, if the distance between the two objects is doubled, the force of gravity they exert on each other will decrease by a factor of 2^2 = 4, making the force 1/4 as large as it was before.

Question 13

If the masses of the Sun and Earth each were doubled,the force of gravity between them would

Accepted Answer

The force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. Therefore, if the masses of the Sun and Earth each were doubled, the force of gravity between them would increase by a factor of 4 (2 x 2), since the masses in the equation have doubled.

Question 14

An object speeds up in such a way that its acceleration is constant.What can we say about the force acting on the object?

Accepted Answer

According to Newton's second law of motion, when an object experiences a constant acceleration, the force acting on it is also constant. Therefore, the correct answer is B.

Question 15

Suppose an artificial satellite is in a circular orbit about the Earth.What can be said about the acceleration of the satellite?

Accepted Answer

The satellite is accelerating because, even though its speed might remain constant, its direction is constantly changing as it moves in a circular orbit. This change in direction means there is a centripetal acceleration directed towards the center of the orbit, which is a characteristic of circular motion.

Question 16

Suppose the Earth were moved to Mercury's distance from the Sun (0.4 AU).How would the gravitational force between the Earth and Sun then compare to its present value?

Accepted Answer

According to the law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Since the distance between the Earth and Sun changes from 1 AU to 0.4 AU, the gravitational force between them would be [(1/0.4)^2] = 6.25 times as strong as its present value.

Question 17

When a force is applied to a body with a mass of 100 kg,the acceleration of the body is 1 m/s/s.If the same force is applied to a body with a mass of 40 kg,what is the acceleration of the body?

Accepted Answer

According to Newton's second law of motion, $F = ma$, where $F$ is the force applied, $m$ is the mass of the object, and $a$ is the acceleration. If the same force is applied to a lighter object, the acceleration increases. For the 100 kg mass, $a = 1 m/s^2$. For the 40 kg mass, using the proportion $100 kg : 1 m/s^2 = 40 kg : x m/s^2$, solving for $x$ gives $x = 2.5 m/s^2$.

Question 18

Compared with your mass on Earth,your mass on the Moon would be

Accepted Answer

Your mass remains constant regardless of your location in the universe. It is your weight that changes due to the difference in gravitational force, not your mass.

Question 19

The radius of the Moon is one-fourth that of the Earth,and its mass is 1.3 percent of the Earth's mass.If you were standing on the surface of the Moon,what would your weight be?

Accepted Answer

The gravitational force (weight) on an object is directly proportional to the mass of the body (in this case, the Moon) and inversely proportional to the square of the radius. Since the Moon's mass is 1.3% (or 0.013) of the Earth's and its radius is 1/4 of the Earth's, the weight of an object on the Moon would be $0.013 \times (4^2) = 0.013 \times 16 = 0.208$, or approximately 20% of its weight on Earth.

Question 20

What is centripetal force?

Accepted Answer

Centripetal force is the force required to keep an object moving in a circular path. It is directed towards the center of the circular path and is responsible for constantly changing the direction of the object's velocity, even though its speed may remain constant.

Quiz 5: Gravity and Motion