How does the kinetic energy of an object change if its momentum is doubled ? Show with the help of an example that gravitational potential energy is independent of path followed?

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How does the kinetic energy of an object change if its momentum is doubled ? Show with the help of an example that gravitational potential energy is independent of path followed?

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How does the kinetic energy of an object change if its momentum is dou...

The kinetic energy of an object is equal to the product of its mass and the square of its velocity. If the momentum of an object is doubled, the velocity of the object will also be doubled, assuming that the mass of the object remains constant. Therefore, the kinetic energy of the object will be quadrupled.

For example, consider a bowling ball with a mass of 5 kilograms that is rolling down a lane with a velocity of 5 meters per second. The kinetic energy of the ball is equal to (1/2) * 5 kilograms * (5 meters per second)^2 = 125 Joules. If the momentum of the ball is doubled, the velocity of the ball will also be doubled to 10 meters per second. The kinetic energy of the ball will then be (1/2) * 5 kilograms * (10 meters per second)^2 = 500 Joules, which is four times the original value.

Gravitational potential energy is the energy that an object possesses due to its position in a gravitational field. It is equal to the product of the mass of the object, the acceleration due to gravity, and the height of the object above a reference point. The path followed by the object does not affect the gravitational potential energy of the object, as long as the height of the object above the reference point is the same.

For example, consider a bowling ball that is lifted to a height of 10 meters above the ground. The gravitational potential energy of the ball is equal to the product of its mass, the acceleration due to gravity, and the height above the ground, which is equal to 5 kilograms * 9.8 meters/second^2 * 10 meters = 490 Joules. If the ball is lifted to the same height using a different path, such as a curved path or a zig-zag path, the gravitational potential energy of the ball will still be 490 Joules.

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