An asteroid is moving along a straight line. A force acts...

An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of $4.5 \times 10^{4} \mathrm{kg},$ and the force causes its speed to change from 7100 to $5500 \mathrm{m} / \mathrm{s}$ (a) What is the work done by the force? (b) If the asteroid slows down over a distance of $1.8 \times 10^{6} \mathrm{m},$ determine the magnitude of the force.

An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of $4.5 \times 10^{4} \mathrm{kg},$ and the force causes its speed to change from 7100 to $5500 \mathrm{m} / \mathrm{s}$
(a) What is the work done by the force? (b) If the asteroid slows down over a distance of $1.8 \times 10^{6} \mathrm{m},$ determine the magnitude of the force.

Key Concepts

Work-Energy Theorem

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. This principle is essential in solving problems where a force causes a change in speed, as it connects the concepts of work and kinetic energy and allows for the calculation of one quantity if the other is known.

Force and Displacement Relationship

When a constant force causes a change in an object's kinetic energy over a known displacement, the force can be determined by dividing the work done by the displacement. This relationship is pivotal for analyzing situations where the effect of a force is distributed over a distance, allowing one to calculate the magnitude of the force based on energy considerations.

Work

Work is defined as the transfer of energy through the application of a force along a displacement. It is calculated as the product of the force and the distance over which the force is applied, taking into account the direction of the force relative to the displacement. This concept is important because it links force and displacement to a change in the energy of an object.

Kinetic Energy

Kinetic energy is the energy that an object has due to its motion, and it is calculated using the formula (1/2)mv², where m is the mass and v is the velocity. This concept is crucial as it provides a way to quantify how much motion an object has at any given speed, allowing comparison of energy before and after any change in velocity.

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