Calculating Arrow Speed with Doubled Force | Newton's Law Problem

In summary, when the average force exerted on an arrow leaving a bow is doubled, the acceleration also doubles, but the resulting velocity does not double. To find the new velocity, the initial acceleration must be calculated and then plugged into the equation vf = vi + at. Using the work done and conservation of energy, it can be determined that the new velocity is directly proportional to the force applied.
  • #1
ethrust2
3
0

Homework Statement


An arrow, starting from rest, leaves the bow with a speed of 29.5 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?


Homework Equations



use a= v-vo/t and f=ma

The Attempt at a Solution



i tried to just multiply the speed by 2 but that's wrong... and the same speed is wrong too..
 
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  • #2
F = ma
If the force doubled, then the acceleration must double, because the mass definitely can't double xD

So, that means the new acceleration is twice the initial acceleration. This doesn't mean the new velocity is twice the old velocity.

First, let's find the initial acceleration.
vf = vi + at
29.5 = 0 + at
ai = 59/t

The new acceleration is twice the initial acceleration, so
anew = (2*59)/t = 118/t
anew = = 118/t

Now, plugging that back into the equation:
vf = vi + at
vf = 29.5 + (118/t)*t ===> Note how the t cancels out
vf = 29.5 + 118
vf = 147.5 m/s
 
  • #3
thanks so much man
 
  • #4
Welcome to PF!

Hi Firecloak! Welcome to PF! :smile:

Sorry, but your method is completely wrong …

vi is still zero, not 29.5; and it isn't the same t. :redface:

Hi ethrust2! :wink:

The distance will be the same (exactly the same if it's a crossbow, and almost exactly if it's a longbow) …

so … using work done and conservation of energy … how does v depend on F? :smile:
 

Related to Calculating Arrow Speed with Doubled Force | Newton's Law Problem

1. What is the first law of motion according to Newton's law?

The first law of motion, also known as the law of inertia, states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

2. How do you calculate force using Newton's second law?

The formula for calculating force using Newton's second law is F=ma, where F is the force, m is the mass of the object, and a is the acceleration.

3. Can you give an example of a simple Newton law problem?

One example would be a car traveling at a constant speed of 60 km/h. If the car has a mass of 1000 kg, what is the force needed to keep it moving at this speed? Using the formula F=ma, we can calculate that the force needed is 60,000 N.

4. How does Newton's third law explain the relationship between action and reaction?

Newton's third law 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.

5. What is the significance of understanding Newton's laws of motion?

Understanding Newton's laws of motion is crucial in understanding the fundamental principles of physics and how objects behave in motion. These laws are used to explain and predict the motion of objects, and are the basis for many engineering and technological advancements.

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