Question

An 82 g arrow is fired from a bow whose string exerts an average force of 95 N on the arrow over a distance of 85 cm. What is the speed of the arrow as it leaves the bow?
Express as m/s

Answer 1

Concepts and reason

The concepts used to solve this problem are work-energy theorem, kinetic energy, and work done.

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First, use the expression for work done related by the change in kinetic energy to find the expression

Then, use the work-energy expression obtained in the above expression and rearrange to find the velocity of the arrow.

Fundamentals

The expression for kinetic energy is as follows:

Here, kinetic energy is , mass of the particle is , and its velocity is .

According to the work-energy theorem, “the work done on an object by a net force equals the change in kinetic energy of the object”.

The expression for work-energy theorem is as follows:

$W=K,-K $

Here, the work done is , the initial kinetic energy is , and the final kinetic energy is .

The work done is as follows:

Here, the work done is , the force is , the displacement is , and the angle between the force and displacement is .

According to the work-energy theorem, “the work done on an object by a net force equals the change in kinetic energy of the object”.

The work done is as follows:

…… (1)

The expression for work-energy theorem is as follows:

$W=K,-K $ …… (2)

The electron has a negligible initial velocity, and hence the initial kinetic energy can be neglected.

Thus, the initial kinetic energy is as follows:

The final kinetic energy is given by the following expression:

Substitute the above kinetic energy expressions and work done expression in Equation (1) and Equation (2).

The obtained work-energy expression is as follows:

Rearrange the above expression.

Substitute for, for , and for

Ans:

The final velocity of the arrow is .