Calculating Deceleration and Penetration Distance of Arrow in Styrofoam Block

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In summary, an arrow with a speed of 22.0 m/s is fired at a block of Styrofoam on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it. The arrow's deceleration has a magnitude of 1570 m/s^2 and the block's acceleration has a magnitude of 450 m/s^2. To find the time it takes for the arrow to stop moving with respect to the block, the equations v = u - a*t and v = 0 + a*t can be used for the arrow and block respectively. The common speed of the arrow and block when this happens can be found by solving for v and t. For part c
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Homework Statement


An arrow is fired with a speed of 22.0 m/s at a block of Styrofoam resting on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it. During this process the arrow's deceleration has a magnitude of 1570 m/s^2 and the block's acceleration has a magnitude of 450 m/s^2.
a)How long does it take for the arrow to stop moving with respect to the block?
b)What is the common speed of the arrow and block when this happens?
c)How far into the block does the arrow penetrate?

Homework Equations


I tried doing a= v/t. to find the time. but the answer wasnt right. i really don't know where to start for it.

The Attempt at a Solution


I need help on parts a and b. i really have no ideas what to do.
 
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i just need a formula to get going.
 
  • #3
For arrow, v= u -a1*t. For block, v = 0 + a2*t. You find v and t. Enough?
 

FAQ: Calculating Deceleration and Penetration Distance of Arrow in Styrofoam Block

1. What is the "arrow goes into block" phenomenon?

The "arrow goes into block" phenomenon, also known as the "arrow in the block" experiment, refers to a classic physics demonstration where a wooden block is placed on a smooth surface and an arrow is shot into the block. The arrow is seen to penetrate the block and remain stuck in it, rather than continuing to travel through or bounce off of it.

2. How does this phenomenon relate to the laws of physics?

The "arrow goes into block" demonstration is a clear example of the conservation of momentum and energy. The arrow, being a smaller and lighter object, has a higher velocity than the block. Upon impact, the momentum and energy of the arrow is transferred to the block, causing it to move forward and the arrow to become embedded in it.

3. What factors affect the outcome of the experiment?

The outcome of the "arrow goes into block" experiment can be affected by various factors such as the mass and velocity of the arrow, the mass and composition of the block, and the surface on which the block is resting. The angle and accuracy of the shot can also play a role in the final result.

4. Can this experiment be replicated with different objects?

Yes, the "arrow goes into block" experiment can be replicated with different objects as long as they have the same properties and follow the laws of physics. For example, instead of an arrow and a wooden block, one could use a dart and a foam block or a bullet and a clay block. The end result should be similar, with the smaller object becoming embedded in the larger one.

5. What practical applications does this phenomenon have?

The "arrow goes into block" experiment may seem like a simple demonstration, but it has practical applications in fields such as ballistics and engineering. Understanding the laws of physics involved in this phenomenon can help in the design and improvement of materials and structures that need to withstand high-velocity impacts.

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