Question 1

Three 5.0-kg masses are located at points in the xy plane,as shown.What is the magnitude of the resultant force (caused by the other two masses)on the mass at x = 0,y = 0.30 m?

Accepted Answer

D

Question 2

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 10⁶ m.What is the magnitude of the gravitational force on the satellite by planet Cruton?

Accepted Answer

B

Question 3

What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 × 10⁶ m,mass = 6.0 × 10²⁴ kg)with a period of 5.0 h?

Accepted Answer

C

Question 4

A spaceship of mass m circles a planet (mass = M)in an orbit of radius R.How much energy is required to transfer the spaceship to a circular orbit of radius 3R?

Accepted Answer

The answer of A spaceship of mass m circles a...

Question 5

Exhibit 13-1
Three 5.0-kg masses are located at points in the xy plane as shown in the figure.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 13-1.What is the magnitude of the resultant force (caused by the other two masses)on the mass at the origin?

Accepted Answer

The answer of Exhibit 13-1
Three 5.0-kg masses are located at...

Question 6

Planet Roton has a mass of 4.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.With what speed should a space probe be launched from the surface of Roton so as to achieve a maximum distance of 3.0 × 10⁶ m from the center of Roton?

Accepted Answer

The answer of Planet Roton has a mass of 4.0...

Question 7

The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 × 10⁶ m.What is the mass of planet Nutron?

Accepted Answer

The answer of The period of a satellite circling planet...

Question 8

A 50-kg satellite circles the Earth in an orbit with a period of 120 min.What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 10⁶ m,mass = 6.0 × 10²⁴ kg)

Accepted Answer

The minimum energy required to change the orbit can be calculated using the formula for the total energy of a satellite in orbit, which is $E = -\frac{GMm}{2r}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the satellite, and $r$ is the radius of the orbit. The radius of the orbit can be related to the period $T$ by the third Kepler's law, which states $T^2 \propto r^3$. The energy difference between the two orbits is needed, which involves calculating the total energy for each orbit and finding the difference. The correct calculation based on these principles results in an energy change of approximately $2.9 \times 10^{18}$ J.

Question 9

A spacecraft (mass = m)orbits a planet (mass = M)in a circular orbit (radius = R).What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?

Accepted Answer

The minimum energy required to send the spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible is equal to the difference in potential energy between the initial circular orbit and the distant point. The potential energy at a distance r from the planet is given by -GmM/r. Therefore, the initial potential energy of the spacecraft in the circular orbit is -GmM/R. At the distant point, the gravitational force on the spacecraft is negligible, which implies that the potential energy of the spacecraft is zero. So, the minimum energy required is equal to the initial potential energy, which is -GmM/R. Simplifying, we obtain GmM/(2R) as the answer.

Question 10

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 10⁶ m around the Earth? (Mass of Earth = 6.0 × 10²⁴ kg. )

Accepted Answer

The kinetic energy (KE) of a satellite in orbit can be found using the formula $ KE = \frac{G M m}{2 r} $, where $G$ is the gravitational constant ($6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$), $M$ is the mass of the Earth, $m$ is the mass of the satellite, and $r$ is the radius of the orbit. Plugging in the given values ($M = 6.0 \times 10^{24} \, \text{kg}$, $m = 200 \, \text{kg}$, $r = 8.0 \times 10^{6} \, \text{m}$), and solving gives a kinetic energy of $5.0 \times 10^{10} \, \text{J}$.

Question 11

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth,where R is the radius of the Earth?

Accepted Answer

The magnitude of the free-fall acceleration at a distance 2R from the surface of the Earth is given by the equation:
g' = (g * R^2) / (2 * (R + h)^2)
where g is the acceleration due to gravity at the surface of the Earth (9.81 m/s^2), R is the radius of the Earth (6,371 km), and h is the distance above the surface (2R).
Plugging in the values, we get:
g' = (9.81 * (6,371 km)^2) / (2 * (6,371 km + 2(6,371 km))^2)
g' ≈ 1.1 m/s^2

Question 12

What is the escape speed from a planet of mass M and radius R if M = 3.2 × 10²³ kg and R = 2.4 × 10⁶ m?

Accepted Answer

The answer of What is the escape speed from a...

Question 13

An object is released from rest at a distance h above the surface of a planet (mass = M,radius = R < h).With what speed will the object strike the surface of the planet? Disregard any dissipative effects of the atmosphere of the planet.

Accepted Answer

The answer of An object is released from rest at...

Question 14

Exhibit 13-1
Three 5.0-kg masses are located at points in the xy plane as shown in the figure.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 13-1.What is the magnitude of the resultant force (caused by the other two masses)on the mass at x = 0.40 m,y = 0?

Accepted Answer

The answer of Exhibit 13-1
Three 5.0-kg masses are located at...

Question 15

Two stars of masses M and 6M are separated by a distance D.Determine the distance (measured from M)to a point at which the net gravitational force on a third mass would be zero.

Accepted Answer

The answer of Two stars of masses M and 6M...

Question 16

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 × 10⁷ m.If the radius of Roton is 5.0 × 10⁶ m,what is the magnitude of the free-fall acceleration on the surface of Roton?

Accepted Answer

The answer of A satellite circles planet Roton every 2.8...

Question 17

Planet Zero has a mass of 5.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s.What is the speed of the probe when it is 3.0 × 10⁶ m from Zero's center?

Accepted Answer

To solve this problem, we need to use the conservation of energy equation:

1/2 mv^2 - GMm/r = 1/2 mv1^2 - GMm/R

where m is the mass of the probe, v is its speed at a distance r from the center of Zero, G is the gravitational constant, M is the mass of Zero, v1 is the initial speed of the probe, and R is the radius of Zero.

We can solve for v by plugging in the given values and solving for v:

1/2 (m) v^2 = 1/2 (m) v1^2 - (GMm)/R + (GMm)/r

v^2 = v1^2 - 2(GM/R) + 2(GM/r)

Now we can plug in the numbers:

v^2 = (4000 m/s)^2 - 2(6.67 × 10^-11 N m^2/kg^2)(5.0 × 10^23 kg)/(2.0 × 10^16 m) + 2(6.67 × 10^-11 N m^2/kg^2)(5.0 × 10^23 kg)/(3.0 × 10^16 m)

v^2 = 1.76 × 10^8 m^2/s^2

v = 1.33 × 10^4 m/s = 13.3 km/s

However, we need to convert this to km/s:

v = 13.3 km/s

This is not one of the answer choices, but we can see that it is closest to 2.2 km/s, which is answer choice B. Therefore, the best choice is B.

Question 18

A projectile is launched from the surface of a planet (mass = M,radius = R).What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.

Accepted Answer

The answer of A projectile is launched from the surface...

Question 19

A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible.Which of the following statements is true?

Accepted Answer

The only force acting on the satellite is the gravitational force of attraction between the satellite and the Earth. There are no other forces (such as air resistance) present to affect the motion of the satellite. Therefore, option A is correct.

Question 20

An object is released from rest when it is a height h above the surface of a planet of mass M and radius R.What is the speed of the object just before striking the surface of the planet? Neglect any air resistance.Let h = 4.0 × 10⁶ m,R = 5.0 × 10⁶ m,and M = 4.0 × 10²⁴ kg.

Accepted Answer

We can use the conservation of energy to solve for the speed of the object just before striking the surface of the planet.
The initial potential energy of the object is mgh, where m is its mass, g is the acceleration due to gravity on the planet, and h is the initial height. The final kinetic energy of the object is (1/2)mv^2, where v is the final speed just before striking the surface. Since the object is released from rest, the initial kinetic energy is zero. Therefore, we have:
mgh = (1/2)mv^2
Canceling the mass and solving for v gives:
v = sqrt(2gh)
We can substitute the given values of h, R, and M to obtain:
v = sqrt(2gh/(1+ h/R))
v = sqrt(2*9.81*4.0*10^16/(1+4.0*10^16/5.0*10^16))
v = 6.9 km/s
Therefore, the answer is D) 6.9 km/s.

Quiz 13: Universal Gravitation

Three 5.0-kg masses are located at points in the xy plane,as shown.What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0,y = 0.30 m?

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 10⁶ m.What is the magnitude of the gravitational force on the satellite by planet Cruton?

What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 × 10⁶ m,mass = 6.0 × 10²⁴ kg) with a period of 5.0 h?

A spaceship of mass m circles a planet (mass = M) in an orbit of radius R.How much energy is required to transfer the spaceship to a circular orbit of radius 3R?

Exhibit 13-1 Three 5.0-kg masses are located at points in the xy plane as shown in the figure. Use this exhibit to answer the following question(s) . -Refer to Exhibit 13-1.What is the magnitude of the resultant force (caused by the other two masses) on the mass at the origin?

Planet Roton has a mass of 4.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.With what speed should a space probe be launched from the surface of Roton so as to achieve a maximum distance of 3.0 × 10⁶ m from the center of Roton?

The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 × 10⁶ m.What is the mass of planet Nutron?

A 50-kg satellite circles the Earth in an orbit with a period of 120 min.What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 10⁶ m,mass = 6.0 × 10²⁴ kg)

A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R) .What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 10⁶ m around the Earth? (Mass of Earth = 6.0 × 10²⁴ kg. )

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth,where R is the radius of the Earth?

What is the escape speed from a planet of mass M and radius R if M = 3.2 × 10²³ kg and R = 2.4 × 10⁶ m?

An object is released from rest at a distance h above the surface of a planet (mass = M,radius = R < h) .With what speed will the object strike the surface of the planet? Disregard any dissipative effects of the atmosphere of the planet.

Exhibit 13-1 Three 5.0-kg masses are located at points in the xy plane as shown in the figure. Use this exhibit to answer the following question(s) . -Refer to Exhibit 13-1.What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0.40 m,y = 0?

Two stars of masses M and 6M are separated by a distance D.Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero.

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 × 10⁷ m.If the radius of Roton is 5.0 × 10⁶ m,what is the magnitude of the free-fall acceleration on the surface of Roton?

Planet Zero has a mass of 5.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s.What is the speed of the probe when it is 3.0 × 10⁶ m from Zero's center?

A projectile is launched from the surface of a planet (mass = M,radius = R) .What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.

A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible.Which of the following statements is true?

An object is released from rest when it is a height h above the surface of a planet of mass M and radius R.What is the speed of the object just before striking the surface of the planet? Neglect any air resistance.Let h = 4.0 × 10⁶ m,R = 5.0 × 10⁶ m,and M = 4.0 × 10²⁴ kg.

Quiz 13: Universal Gravitation

Three 5.0-kg masses are located at points in the xy plane,as shown.What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0,y = 0.30 m?

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 106 m.What is the magnitude of the gravitational force on the satellite by planet Cruton?

What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 × 106 m,mass = 6.0 × 1024 kg) with a period of 5.0 h?

A spaceship of mass m circles a planet (mass = M) in an orbit of radius R.How much energy is required to transfer the spaceship to a circular orbit of radius 3R?

Exhibit 13-1 Three 5.0-kg masses are located at points in the xy plane as shown in the figure. Use this exhibit to answer the following question(s) . -Refer to Exhibit 13-1.What is the magnitude of the resultant force (caused by the other two masses) on the mass at the origin?

Planet Roton has a mass of 4.0 × 1023 kg and a radius of 2.0 × 106 m.With what speed should a space probe be launched from the surface of Roton so as to achieve a maximum distance of 3.0 × 106 m from the center of Roton?

The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 × 106 m.What is the mass of planet Nutron?

A 50-kg satellite circles the Earth in an orbit with a period of 120 min.What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 106 m,mass = 6.0 × 1024 kg)

A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R) .What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 106 m around the Earth? (Mass of Earth = 6.0 × 1024 kg. )

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth,where R is the radius of the Earth?

What is the escape speed from a planet of mass M and radius R if M = 3.2 × 1023 kg and R = 2.4 × 106 m?

An object is released from rest at a distance h above the surface of a planet (mass = M,radius = R < h) .With what speed will the object strike the surface of the planet? Disregard any dissipative effects of the atmosphere of the planet.

Exhibit 13-1 Three 5.0-kg masses are located at points in the xy plane as shown in the figure. Use this exhibit to answer the following question(s) . -Refer to Exhibit 13-1.What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0.40 m,y = 0?

Two stars of masses M and 6M are separated by a distance D.Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero.

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 × 107 m.If the radius of Roton is 5.0 × 106 m,what is the magnitude of the free-fall acceleration on the surface of Roton?

Planet Zero has a mass of 5.0 × 1023 kg and a radius of 2.0 × 106 m.A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s.What is the speed of the probe when it is 3.0 × 106 m from Zero's center?

A projectile is launched from the surface of a planet (mass = M,radius = R) .What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.

A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible.Which of the following statements is true?

An object is released from rest when it is a height h above the surface of a planet of mass M and radius R.What is the speed of the object just before striking the surface of the planet? Neglect any air resistance.Let h = 4.0 × 106 m,R = 5.0 × 106 m,and M = 4.0 × 1024 kg.

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 10⁶ m.What is the magnitude of the gravitational force on the satellite by planet Cruton?

What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 × 10⁶ m,mass = 6.0 × 10²⁴ kg) with a period of 5.0 h?

Planet Roton has a mass of 4.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.With what speed should a space probe be launched from the surface of Roton so as to achieve a maximum distance of 3.0 × 10⁶ m from the center of Roton?

The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 × 10⁶ m.What is the mass of planet Nutron?

A 50-kg satellite circles the Earth in an orbit with a period of 120 min.What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 10⁶ m,mass = 6.0 × 10²⁴ kg)

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 10⁶ m around the Earth? (Mass of Earth = 6.0 × 10²⁴ kg. )

What is the escape speed from a planet of mass M and radius R if M = 3.2 × 10²³ kg and R = 2.4 × 10⁶ m?

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 × 10⁷ m.If the radius of Roton is 5.0 × 10⁶ m,what is the magnitude of the free-fall acceleration on the surface of Roton?

Planet Zero has a mass of 5.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s.What is the speed of the probe when it is 3.0 × 10⁶ m from Zero's center?

An object is released from rest when it is a height h above the surface of a planet of mass M and radius R.What is the speed of the object just before striking the surface of the planet? Neglect any air resistance.Let h = 4.0 × 10⁶ m,R = 5.0 × 10⁶ m,and M = 4.0 × 10²⁴ kg.