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The vertical component of the acceleration of a sailplane is zero when the air pushes up against its wings with a force of 3.16 kN. Assuming that the only forces on the sailplane are that due to gravity and that due to the air pushing against its wings, what is the gravitational force on the Earth due to the sailplane (enter first)? Is that force upward or downward?

Question

The vertical component of the acceleration of a sailplane is zero when the air pushes up against its wings with a force of 3.16 kN. Assuming that the only forces on the sailplane are that due to gravity and that due to the air pushing against its wings, what is the gravitational force on the Earth due to the sailplane (enter first)? Is that force upward or downward?

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Solution 1

The gravitational force on the Earth due to the sailplane can be calculated using Newton's second law of motion, which states that the force on an object is equal to its mass times its acceleration. In this case, the force is the force of gravity, which is equal to the mass of the sailplane times the acceleration due to gravity.

Given that the vertical component of the acceleration of the sailplane is zero, this means that the force of the air pushing up against its wings is equal to the force of gravity pulling it down. Therefore, the gravitational force on the Earth due to the sailplane is equal to the force of the air pushing up against its wings, which is given as 3.16 kN.

As for the direction of this force, according to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that if the Earth is exerting a downward force on the sailplane (which is the force of gravity), then the sailplane is exerting an equal force upward on the Earth. Therefore, the gravitational force on the Earth due to the sailplane is upward.

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Solution 2

The gravitational force on the Earth due to the sailplane can be calculated using Newton's second law of motion, which states that the force on an object is equal to its mass times its acceleration.

In this case, the sailplane is not accelerating vertically, which means the net force on it in the vertical direction is zero. This means the force of the air pushing up on the sailplane (3.16 kN) must be equal to the force of gravity pulling it down.

Therefore, the gravitational force on the Earth due to the sailplane is also 3.16 kN.

As for the direction of this force, according to Newton's third law of motion, every action has an equal and opposite reaction. This means that if the Earth is exerting a downward force on the sailplane (gravity), the sailplane is exerting an equal upward force on the Earth. So, the force is upward.

This problem has been solved

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