"Calculating the Velocity of an Arrow Hitting Hay

  • Thread starter lking226
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In summary, the problem involves a 1kg arrow hitting a bail of hay and penetrating 47.0cm. The average frictional force of the hay on the arrow is 2500.0N. To find the original velocity of the arrow, we can use the equation Ffr = uk x Fn and the kinetic energy-work theorem, where the work done is negative due to the decrease in kinetic energy.
  • #1
lking226
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Homework Statement


A 1kg arrow hits a bail of hay and penetrates 47.0cm. The average frictional force of the hay on the arrow is 2500.0N. What was the original velocity of the arrow?


Homework Equations


Ffr = uk x Fn


The Attempt at a Solution


I'm completely lost, can someone please walk me through this?
 
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  • #2
Well we know that,

W = fdcos(theta).

cos(theta) is going to go to 1 so,

W = fd.

We're given then average force and the distance so we can solve for the work done.

After you've done that I want you to think about the kinetic energy - work theorem ;)
 
  • #3
is the kinetic energy-work theorem net work = change in kinetic energy?
so then, w = 1/2mvf^2-1/2mvi^2, but vf is 0 because the arrow is stopped in the hay so really w = -1/2mvi^2. does that stay negative?
 
  • #4
lking226 said:
is the kinetic energy-work theorem net work = change in kinetic energy?
so then, w = 1/2mvf^2-1/2mvi^2, but vf is 0 because the arrow is stopped in the hay so really w = -1/2mvi^2. does that stay negative?

Yes, the work done is negative, because the kinetic energy decreaes (in this case all the way to zero, so that the change in kinetic energy is just the negative of how much there was to start with).
 
  • #5
got it, thanks guys!
 

FAQ: "Calculating the Velocity of an Arrow Hitting Hay

1. How do you calculate the velocity of an arrow hitting hay?

To calculate the velocity of an arrow hitting hay, you will need to measure the distance the arrow travels and the time it takes to travel that distance. You can then use the formula velocity = distance / time to determine the velocity of the arrow.

2. What units should be used to measure the distance and time?

The distance should be measured in meters and the time should be measured in seconds. This will ensure that the velocity is calculated in meters per second (m/s).

3. Is the velocity of an arrow hitting hay affected by the weight of the arrow?

Yes, the velocity of an arrow hitting hay is affected by the weight of the arrow. Heavier arrows will have a slower velocity compared to lighter arrows when fired with the same amount of force. This is because heavier objects require more force to accelerate.

4. What other factors can affect the velocity of an arrow hitting hay?

The velocity of an arrow hitting hay can also be affected by the force with which it is launched, air resistance, and the angle at which it is launched. These factors can vary depending on the type of bow used and the environmental conditions.

5. Can the velocity of an arrow hitting hay be used to determine its kinetic energy?

Yes, the velocity of an arrow hitting hay can be used to determine its kinetic energy. The formula for kinetic energy is 1/2 x mass x velocity^2. By calculating the velocity of the arrow and knowing its mass, you can determine its kinetic energy upon impact with the hay.

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