Exam 5: Circular Motion; Gravitation

In another solar system, a planet has a moon that is $4.0 \times 10 ^ { 5 } \mathrm {~m}$ in diameter. Measurements reveal that this moon takes $3.0 \times 10 ^ { 5 }$ s to make each orbit of diameter $1.8 \times 10 ^ { 8 } \mathrm {~m}$ What is the mass of the planet? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. The car maintains its speed over the bump. What is the normal Force exerted by the seat of the car on a 60.0-kg passenger when the car is at the top of the bump?

A spaceship with a mass of $2.8 \times 10 ^ { 6 } \mathrm {~kg}$ mass of $5.0 \times 10 ^ { 16 } \mathrm {~kg}$ joining the asteroids and is aimed at the midpoint of that line. What is the net gravitational force exerted by the asteroids on the spaceship when the spaceship is 30 \mathrm{~km} away from that midpoint? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

The innermost satellite of Jupiter orbits the planet with a radius of $422 \times 10 ^ { 3 } \mathrm {~km}$ and a period of 1.77 days. What is the mass of Jupiter? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of Friction?

A satellite having orbital speed V orbits a planet of mass M . If the planet had half as much mass, the orbital speed of the satellite at the same distance from the center would be

An astronaut goes out for a "space-walk" at a distance above the earth equal to the radius of the earth. What is her acceleration due to gravity at that point?

The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is 0.40, what would be the Maximum safe driving speed for this horizontal curved section of highway?

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 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 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle θ is measured to be 18°, what is the speed of the mass?

As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon), how Iarge is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 x $10 ^ { 22 } \mathrm {~kg}$ the distance to the Moon is $3.82 \times 10 ^ { 8 } \mathrm {~m}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } .$

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?

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?

What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ the mass of the Moon is $7.35 \times 10 ^ { 22 } \mathrm {~kg}$ the center-to-center distance between Earth and the Moon is 3.84 \times $10 ^ { 8 } \mathrm {~m}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$

The captain of a spaceship orbiting planet X discovers that to remain in orbit at 410 km from the planet's center, she needs to maintain a speed of 68 m/s . What is the mass of planet X? $( G = 6.67 \times$ $\left. 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

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

From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.54 g ? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , M _ { \text {earth } } = 5.97 \times 10 ^ { 24 } \mathrm {~kg} , R \text { earth } = 6.38 \times \right.$ $10 ^ { 6 } \mathrm {~m} \text { ) }$

Three identical 50-kg balls are held at the corners of an equilateral triangle, 30 cm on each side. If one of the balls is released, what is the magnitude of its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

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?