Question 1

What is the gravitational force between two nuclei, each of mass 3.20 × 10^-27 kg, which are separated by a distance of 1.06 × 10^-10 m? (G = 6.67 × 10^-11 N m²/kg²)

Accepted Answer

The gravitational force formula is:

F = G * (m1 * m2) / r^2

Where G is the gravitational constant, m1 and m2 are the masses of the objects and r is the distance between them.

Plugging in the given values:

F = (6.67 × 10^-11 N m^2/kg^2) * (3.20 × 10^-27 kg)^2 / (1.06 × 10^-10 m)^2

F = 6.08 × 10^-44 N

Therefore, the answer is B) 6.08 × 10^-44 N.

Question 2

An object with a mass of 200.0 kg is 500.0 km above the surface of the Earth. The magnitude of the force of gravity on the 200.0 kg mass is (G = 6.67 × 10^-11 N m²/kg², the radius of the Earth is 6.38 × 10⁶ m, and the mass of the Earth is 5.98 × 10²⁴ kg)

Accepted Answer

The force of gravity on the object can be calculated using the formula:

F = G * (m1 * m2) / r^2

where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, m1 is the mass of the object (200.0 kg), m2 is the mass of the Earth (5.98 × 10^24 kg), and r is the distance from the center of the Earth to the object (radius of the Earth + height of object above the surface of the Earth):
r = 6.38 × 10^6 m + 5.00 × 10^5 m = 6.88 × 10^6 m

Substituting these values into the formula:
F = (6.67 × 10^-11 N m^2/kg^2) * (200.0 kg) * (5.98 × 10^24 kg) / (6.88 × 10^6 m)^2
F = 1.69 × 10^13 N

Therefore, the magnitude of the force of gravity on the 200.0 kg mass is 1.69 × 10^13 N. The correct answer is B).

Question 3

A mass sits at rest on top of a table. Which two forces are interaction pair forces and thus are equal and opposite?

Accepted Answer

According to Newton's third law, interaction pair forces are equal and opposite. The force of gravity on the mass due to the Earth and the force of gravity on the Earth due to the mass are such a pair.

Question 4

The Moon (mass 7.35 × 10²² kg) is orbiting about the Earth (mass 5.98 × 10²⁴ kg) at a radius of 3.85 × 10⁸ meters. The magnitude of the force of gravity on the Moon due to the Earth is (G = 6.67 × 10^-11 N m²/kg²)

Accepted Answer

The gravitational force between two masses is calculated using the formula $F = \frac{Gm_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers. Substituting the given values: $F = \frac{(6.67 \times 10^{-11}) \times (7.35 \times 10^{22}) \times (5.98 \times 10^{24})}{(3.85 \times 10^{8})^2}$, the calculation yields a force of approximately $1.98 \times 10^{20} N$, which corresponds to choice D.

Question 5

The Moon (mass 7.35 × 10²² kg) orbits the Earth (mass 5.98 × 10²⁴ kg) at a distance of 3.85 × 10⁸ meters. Meanwhile, the Earth orbits the Sun (mass 1.99 × 10³⁰ kg) at a distance of 1.50 × 10¹¹ meters. When the Moon is directly between the Earth and the Sun, what is the gravitational field at the location of the Moon due to the Earth and the Sun combined? (G = 6.67 × 10^-11 N m²/kg²)

Accepted Answer

The answer of The Moon (mass 7.35 × 10²² kg)...

Question 6

What is the gravitational force between two 5.00 kg masses that are 10.0 cm apart from center to center? (G = 6.67 × 10^-11 N m²/kg²)

Accepted Answer

Using the formula for gravitational force: 
F = (G * m1 * m2)/r^2
where F is the force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.

Plugging in the given values: 
F = (6.67 × 10^-11 N m^2/kg^2) * (5.00 kg)^2 / (0.10 m)^2
F = 1.67 × 10^-7 N
which is approximately equal to 1.67 × 10^-7 N = 1.67 × 10^-7 N * 10^4/10^4 = 1.67 × 10^-3 mN.

Therefore, the best choice is B, 1.67 × 10^-7 N.

Question 7

The diagram below represents an ideal pulley system (no mass or friction). What is the force required to lift the 45 kg mass?

Accepted Answer

In an ideal pulley system, the force required to lift a mass is equal to the weight of the mass divided by the number of segments of rope supporting the mass. Since there are two segments of rope supporting the 45 kg mass in this diagram, the force required to lift it is (45 kg x 9.8 m/s²) / 2 = 221.25 N, which can be rounded to 221 N. Therefore, the correct answer is C.

Question 8

Diane (weight 255 N) is practicing on a tightrope that is 6.00 meters long (when unstretched) and sags by 0.120 meters under her weight. When she is in the middle of the rope, what is the force (due to the rope) on each eyebolt holding the tightrope?

Accepted Answer

The answer of Diane (weight 255 N) is practicing on...

Question 9

The gravitational field at the Moon due to the Earth is approximately (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the distance to the Moon is 3.85 × 10⁸ m)

Accepted Answer

The formula to calculate the gravitational field is:
g = GM/r^2
where g is the gravitational field, G is the gravitational constant, M is the mass of the Earth, and r is the distance between the Earth and the Moon.
Substituting the given values in the above formula,
g = (6.67 × 10^-11 N m^2/kg^2) × (5.98 × 10^24 kg) / (3.85 × 10^8 m)^2
g = 2.69 × 10^-3 N/kg
The gravitational field is directed towards the Earth, hence the answer is option A.

Question 10

In the figure, an airport luggage carrying train with a tractor T is pulling three luggage carts, M₁, M₂, and M₃, with constant velocity of 4.5 m/s. If T = 300 kg, M₁ = 200 kg, M₂ = 100 kg, and M₃ = 100 kg (there is no friction), then the force in the connection between the tractor T and cart M₁ is

Accepted Answer

The answer of In the figure, an airport luggage carrying...

Question 11

A space probe leaves the solar system to explore interstellar space. Once it is far from any stars, when must it fire its rocket engines?

Accepted Answer

In space, a probe must fire its engines to change its state of motion, including speeding up, slowing down, or changing direction. Newton's first law of motion states that an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Thus, the engines are needed for any change in velocity or direction.

Question 12

Interaction partners

Accepted Answer

Interaction partners, according to Newton's third law of motion, are equal in magnitude and opposite in direction but act on different objects. This principle explains how forces come in pairs that interact between two distinct entities.

Question 13

What is the gravitational field strength at the location of a satellite that is orbiting the Earth at an altitude of 5,000 km? (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the radius of the Earth is 6.38 × 10⁶ m.)

Accepted Answer

The gravitational field strength at a distance r from the center of the Earth is given by:

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

where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the location of interest.

In this case, we are interested in the gravitational field strength at a distance of 5,000 km above the surface of the Earth. The total distance from the center of the Earth to this location is:

$r = R_{Earth} + 5,000 	ext{ km}$

where $R_{Earth}$ is the radius of the Earth.

Substituting the given values, we get:

$r = 6.38 	imes 10^6 	ext{ m} + 5.00 	imes 10^6 	ext{ m} = 1.338 	imes 10^7 	ext{ m}$

$g = \frac{G M}{r^2} = \frac{(6.67 	imes 10^{-11} N \cdot m^2/kg^2)(5.98 	imes 10^{24} kg)}{(1.338 	imes 10^7 	ext{ m})^2} \approx 3.08 	ext{ N/kg}$

Therefore, the best choice is C.

Question 14

When an object is in translational equilibrium, which of these statements is not true?

Accepted Answer

Translational equilibrium means the net force acting on an object is zero, which allows for both stationary objects and objects moving at constant velocity. Being stationary is not a requirement, thus B is not true.

Question 15

A large massive rock is in contact with the Earth. Draw a force diagram for the rock and the Earth. Which of the following statements is true?

Accepted Answer

According to Newton's third law, every action has an equal and opposite reaction. The gravitational force on the rock due to the Earth and the gravitational force on the Earth due to the rock are equal in magnitude and opposite in direction, and therefore they are interaction partners. The contact force on the Earth due to the rock is not an action-reaction pair with the gravitational force, as it is a separate force that arises from the contact between the two objects.

Question 16

What is the gravitational field strength on the surface of the Earth? (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the radius of the Earth is 6.38 × 10⁶ m.)

Accepted Answer

The gravitational field strength on the surface of the Earth can be calculated using the formula,
g = G * (M / R^2), where
g = gravitational field strength
G = universal gravitational constant
M = mass of the Earth
R = radius of the Earth

Substituting the given values, we get
g = 6.67 × 10^-11 * (5.98 × 10^24) / (6.38 × 10^6)^2
g = 9.80 N/kg

Therefore, the best choice is C, 9.80 N/kg.

Question 17

The gravitational field at the Earth due to the Moon is about (G = 6.67 × 10^-11 N m²/kg², the mass of the Moon is 7.35 × 10²² kg, and the distance to the Moon is 3.85 × 10⁸ m)

Accepted Answer

The gravitational field at a point due to a massive object is given by the formula g = G(M/r^2), where M is the mass of the object, r is the distance from the object, and G is the gravitational constant. In this case, the gravitational field at Earth due to the Moon can be calculated as:

g = (6.67 × 10^-11 N m^2/kg^2)(7.35 × 10^22 kg)/(3.85 × 10^8 m)^2
g = 2.70 × 10^-5 N/kg

Since the Earth is attracted towards the Moon, the gravitational field should be directed towards the Moon. Therefore, the best choice is B: 3.31 × 10^-5 N/kg toward the Moon.

Question 18

Causing an object to start moving on a frictional surface requires

Accepted Answer

This statement is given in the concept of physics that to start an object moving on a frictional surface requires more force than is needed to keep it moving on the surface. This is because when the object is at rest, the force of static friction is greater than the force trying to move the object. Initially, when force is applied, the force of static friction for the object is overcome. However, once the object is in motion, the force required to keep it moving is less than the force required to start it moving.

Question 19

Five children are pushing on a snowball; each pushes with a force of magnitude 10.0 N, and each is pushing at an angle of 45° relative to his neighbor. What is the magnitude of the net push on the ball?

Accepted Answer

Since each child is pushing at an angle of 45° relative to their neighbor, the forces they are applying are perpendicular to each other. Therefore, we can use the Pythagorean theorem to find the net force:

F_net = √[(F1 + F2cos(45°))^2 + (F2sin(45°) + F3cos(45°))^2 + (F3sin(45°) + F4cos(45°))^2 + (F4sin(45°) + F5cos(45°))^2 + F5sin(45°)^2]

F_net = √[(10 + 10cos(45°))^2 + (10sin(45°) + 10cos(45°))^2 + (10sin(45°) + 10cos(45°))^2 + (10sin(45°) + 10cos(45°))^2 + 10sin(45°)^2]

F_net = √[(10 + 10/√2)^2 + (10/√2 + 10/√2)^2 + (10/√2 + 10/√2)^2 + (10/√2 + 10/√2)^2 + 10/2]

F_net = √[24.1^2]

F_net = 24.1 N

Therefore, the magnitude of the net push on the ball is 24.1 N, which is closest to choice B.

Question 20

A force of 15 N toward the WEST is applied to a 4.0 kg box. Another force of 42 N toward the EAST is also applied to the 4.0 kg box. The net force on the 4.0 kg box is

Accepted Answer

The net force is calculated by subtracting the smaller force from the larger force and taking the direction of the larger force. Here, 42 N (EAST) - 15 N (WEST) = 27 N toward the EAST.

Quiz 4: Force and Newtons Laws of Motion

What is the gravitational force between two nuclei, each of mass 3.20 × 10^-27 kg, which are separated by a distance of 1.06 × 10^-10 m? (G = 6.67 × 10^-11 N m²/kg²)

An object with a mass of 200.0 kg is 500.0 km above the surface of the Earth. The magnitude of the force of gravity on the 200.0 kg mass is (G = 6.67 × 10^-11 N m²/kg², the radius of the Earth is 6.38 × 10⁶ m, and the mass of the Earth is 5.98 × 10²⁴ kg)

A mass sits at rest on top of a table. Which two forces are interaction pair forces and thus are equal and opposite?

The Moon (mass 7.35 × 10²² kg) is orbiting about the Earth (mass 5.98 × 10²⁴ kg) at a radius of 3.85 × 10⁸ meters. The magnitude of the force of gravity on the Moon due to the Earth is (G = 6.67 × 10^-11 N m²/kg²)

What is the gravitational force between two 5.00 kg masses that are 10.0 cm apart from center to center? (G = 6.67 × 10^-11 N m²/kg²)

The diagram below represents an ideal pulley system (no mass or friction) . What is the force required to lift the 45 kg mass?

Diane (weight 255 N) is practicing on a tightrope that is 6.00 meters long (when unstretched) and sags by 0.120 meters under her weight. When she is in the middle of the rope, what is the force (due to the rope) on each eyebolt holding the tightrope?

The gravitational field at the Moon due to the Earth is approximately (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the distance to the Moon is 3.85 × 10⁸ m)

A space probe leaves the solar system to explore interstellar space. Once it is far from any stars, when must it fire its rocket engines?

Interaction partners

What is the gravitational field strength at the location of a satellite that is orbiting the Earth at an altitude of 5,000 km? (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the radius of the Earth is 6.38 × 10⁶ m.)

When an object is in translational equilibrium, which of these statements is not true?

A large massive rock is in contact with the Earth. Draw a force diagram for the rock and the Earth. Which of the following statements is true?

What is the gravitational field strength on the surface of the Earth? (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the radius of the Earth is 6.38 × 10⁶ m.)

The gravitational field at the Earth due to the Moon is about (G = 6.67 × 10^-11 N m²/kg², the mass of the Moon is 7.35 × 10²² kg, and the distance to the Moon is 3.85 × 10⁸ m)

Causing an object to start moving on a frictional surface requires

Five children are pushing on a snowball; each pushes with a force of magnitude 10.0 N, and each is pushing at an angle of 45° relative to his neighbor. What is the magnitude of the net push on the ball?

A force of 15 N toward the WEST is applied to a 4.0 kg box. Another force of 42 N toward the EAST is also applied to the 4.0 kg box. The net force on the 4.0 kg box is

Quiz 4: Force and Newtons Laws of Motion

What is the gravitational force between two nuclei, each of mass 3.20 × 10-27 kg, which are separated by a distance of 1.06 × 10-10 m? (G = 6.67 × 10-11 N m2/kg2)

An object with a mass of 200.0 kg is 500.0 km above the surface of the Earth. The magnitude of the force of gravity on the 200.0 kg mass is (G = 6.67 × 10-11 N m2/kg2, the radius of the Earth is 6.38 × 106 m, and the mass of the Earth is 5.98 × 1024 kg)

A mass sits at rest on top of a table. Which two forces are interaction pair forces and thus are equal and opposite?

The Moon (mass 7.35 × 1022 kg) is orbiting about the Earth (mass 5.98 × 1024 kg) at a radius of 3.85 × 108 meters. The magnitude of the force of gravity on the Moon due to the Earth is (G = 6.67 × 10-11 N m2/kg2)

What is the gravitational force between two 5.00 kg masses that are 10.0 cm apart from center to center? (G = 6.67 × 10-11 N m2/kg2)

The diagram below represents an ideal pulley system (no mass or friction) . What is the force required to lift the 45 kg mass?

Diane (weight 255 N) is practicing on a tightrope that is 6.00 meters long (when unstretched) and sags by 0.120 meters under her weight. When she is in the middle of the rope, what is the force (due to the rope) on each eyebolt holding the tightrope?

The gravitational field at the Moon due to the Earth is approximately (G = 6.67 × 10-11 N m2/kg2, the mass of the Earth is 5.98 × 1024 kg, and the distance to the Moon is 3.85 × 108 m)

A space probe leaves the solar system to explore interstellar space. Once it is far from any stars, when must it fire its rocket engines?

Interaction partners

What is the gravitational field strength at the location of a satellite that is orbiting the Earth at an altitude of 5,000 km? (G = 6.67 × 10-11 N m2/kg2, the mass of the Earth is 5.98 × 1024 kg, and the radius of the Earth is 6.38 × 106 m.)

When an object is in translational equilibrium, which of these statements is not true?

A large massive rock is in contact with the Earth. Draw a force diagram for the rock and the Earth. Which of the following statements is true?

What is the gravitational field strength on the surface of the Earth? (G = 6.67 × 10-11 N m2/kg2, the mass of the Earth is 5.98 × 1024 kg, and the radius of the Earth is 6.38 × 106 m.)

The gravitational field at the Earth due to the Moon is about (G = 6.67 × 10-11 N m2/kg2, the mass of the Moon is 7.35 × 1022 kg, and the distance to the Moon is 3.85 × 108 m)

Causing an object to start moving on a frictional surface requires

Five children are pushing on a snowball; each pushes with a force of magnitude 10.0 N, and each is pushing at an angle of 45° relative to his neighbor. What is the magnitude of the net push on the ball?

A force of 15 N toward the WEST is applied to a 4.0 kg box. Another force of 42 N toward the EAST is also applied to the 4.0 kg box. The net force on the 4.0 kg box is

What is the gravitational force between two nuclei, each of mass 3.20 × 10^-27 kg, which are separated by a distance of 1.06 × 10^-10 m? (G = 6.67 × 10^-11 N m²/kg²)

An object with a mass of 200.0 kg is 500.0 km above the surface of the Earth. The magnitude of the force of gravity on the 200.0 kg mass is (G = 6.67 × 10^-11 N m²/kg², the radius of the Earth is 6.38 × 10⁶ m, and the mass of the Earth is 5.98 × 10²⁴ kg)

The Moon (mass 7.35 × 10²² kg) is orbiting about the Earth (mass 5.98 × 10²⁴ kg) at a radius of 3.85 × 10⁸ meters. The magnitude of the force of gravity on the Moon due to the Earth is (G = 6.67 × 10^-11 N m²/kg²)

What is the gravitational force between two 5.00 kg masses that are 10.0 cm apart from center to center? (G = 6.67 × 10^-11 N m²/kg²)

The gravitational field at the Moon due to the Earth is approximately (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the distance to the Moon is 3.85 × 10⁸ m)

What is the gravitational field strength at the location of a satellite that is orbiting the Earth at an altitude of 5,000 km? (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the radius of the Earth is 6.38 × 10⁶ m.)

What is the gravitational field strength on the surface of the Earth? (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the radius of the Earth is 6.38 × 10⁶ m.)

The gravitational field at the Earth due to the Moon is about (G = 6.67 × 10^-11 N m²/kg², the mass of the Moon is 7.35 × 10²² kg, and the distance to the Moon is 3.85 × 10⁸ m)