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Question bank: Gravitation: Gravitational Acceleration

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Question 1:

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Gravitation: Gravitational Acceleration
Question 2:

Medium

An astronaut is on a space mission in an equatorial orbit around an exoplanet. This exoplanet has a radius twice that of Earth and a mass that is eight times the mass of Earth. The acceleration due to gravity on Earth's surface is 9.8 m/s². Considering Newton's Universal Law of Gravitation, which describes the force of attraction between two masses due to gravity, and that gravitational acceleration can be calculated by the formula a = G * (M / r^2), where G is the gravitational constant, M is the planet's mass, and r is the planet's radius, calculate the gravitational acceleration at the equatorial orbit of this exoplanet. Then, discuss the impact that a higher or lower gravitational acceleration would have on the conditions necessary to maintain a stable orbit around this planet, considering both the Physics perspective and the implications for satellite and spacecraft engineering.
Gravitation: Gravitational Acceleration
Question 3:

Medium

A student decides to calculate his gravitational potential energy at the heights of Everest (8,848 meters of altitude) and at the beach at sea level. He knows his mass is 75 kg. Using Earth's average gravitational acceleration (g = 9.8 m/s²), what is the approximate difference in his gravitational potential energy between the two mentioned situations?
Gravitation: Gravitational Acceleration
Question 4:

Medium

Imagine you are in a park, where there is a swing suspended by two ropes, each 3 meters long. A friend challenges you to find out how long it would take for a person to go from the highest point to the lowest point of the swing, treating this situation as a simple pendulum even though it is not exactly. To solve this challenge, follow these steps: (a) consider the Earth flat and use the formula for gravitational acceleration g = 9.8 m/s², (b) apply the formula for the period of a simple pendulum T = 2π√(L/g), where L is the length of the rope and g is the acceleration due to gravity, and (c) divide the period found in (b) in half, thus obtaining the time it takes to move from the highest point to the lowest point of the swing.
Gravitation: Gravitational Acceleration
Question 5:

Easy

A Physics student decides to conduct an experiment to estimate the gravitational acceleration of Earth. He drops a ball from a height of 10 meters and measures the time it takes for the ball to touch the ground. If he timed 1.4 seconds for the ball to reach the ground, what is the closest value of Earth's gravitational acceleration in m/s², according to the experiment? Use the formula: h = 0.5 * g * t².
Gravitation: Gravitational Acceleration
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