# Forces/Newton's Laws of Motion

• Amber430
In summary, the conversation discusses a problem where an arrow leaves a bow with a speed of 26.0 m/s and the average force exerted on the arrow is doubled. The question asks for the new speed of the arrow when the force is doubled. The initial velocity remains at 0 and the final velocity is known. The distance the arrow takes to reach the final speed is the same and the relation between distance, acceleration, and speed is V^2=Vo^2 + 2ax. The acceleration would be 2a and the new speed can be solved for in terms of "a" and "x" or using ratios.
Amber430
This problem really shouldn't be this difficult but for some reason I can't seem to find the answer.

An arrow, starting from rest, leaves the bow with a speed of 26.0 m/s. If the average force exerted on the arrow by the bow were doubled, all else remaining the same, with what speed would the arrow leave the bow?

net force= mass x acceleration

Acceleration is unknown in this question. Velocity (I'm assuming it's the final V?) is known (26.0 m/s). Initial velocity is 0. I know that when force doubles, acceleration doubles. That's about as far as I could get.

Amber430 said:
I know that when force doubles, acceleration doubles.
Good. What quantity remains the same? When they said "all else remaining the same", what could they have been talking about?

The initial velocity remains the same. But the only other variable that is given is final velocity, which would not stay the same.

Hint: The distance the arrow takes to reach the final speed is the same.

How do distance, acceleration, and speed relate?

V^2=Vo^2 + 2ax. But what is x? It isn't known.

All you want to do is compare the final speeds. You don't need to know the actual distance. Just call it x.

But what is the acceleration?

Amber430 said:
But what is the acceleration?
Again, you don't need actual numbers. Call the original acceleration "a". What would be the new acceleration?

It would be 2a

Amber430 said:
It would be 2a
Good. Now solve for the speeds in terms of "a" and "x" and compare. (You can also use ratios.)

## What is Newton's First Law of Motion?

Newton's First Law of Motion, also known as the Law of Inertia, states that an object will remain at rest or in constant motion at a constant velocity unless acted upon by an external force.

## What is Newton's Second Law of Motion?

Newton's Second Law of Motion states that the force applied to an object is directly proportional to its mass and acceleration. This means that the greater the mass of an object, the more force is needed to accelerate it, and the greater the acceleration, the more force is needed.

## What is Newton's Third Law of Motion?

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

## What is the difference between mass and weight?

Mass is the amount of matter in an object, while weight is the force of gravity acting on an object. Mass is measured in kilograms, while weight is measured in Newtons. Mass does not change with location, but weight can change depending on the strength of gravity.

## How do forces affect motion?

Forces can cause an object to start moving, stop moving, or change direction. They can also change the speed or velocity of an object. In general, forces cause changes in an object's motion, whether it be in its speed, direction, or both.

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