Circular Motion: Change in Height, Box Struck by Arrow

In summary, an arrow with a velocity of 21.00 m/s will strike a box suspended from a rope, causing the box to experience a new initial velocity of 4.82 m/s. To calculate the maximum change in height the box will experience, the equation for kinetic energy must be used and potential energy can be neglected. The final answer will only require the consideration of the change in height (Δy).
  • #1
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Homework Statement



A box of mass 4.750Kg is suspended from a rope which is attached to the ceiling and is currently at rest. You then shoot an arrow horizontally with a velocity of 21.00 m/s toward the box while standing 4.5m away from it. You may neglect air resistance.

A. With what velocity will the arow strike the box?
B. If the arrow has a mass of 0.2500Kg, what is the max change in height the box theoretically will experience?

Homework Equations



b = Box, a = arrow

KEib + KEfb = KEia + KEfa

Fc = MV^2/r

Fg = mg

The Attempt at a Solution



So what I did was I first solved for the Final Velocity of the box which would become the new initial velocity after the arrow struck the box using the KEib + KEfb = KEia + KEfa.

0.5(4.750)V^2 = 0.5(0.25)(21.00)^2

Solving for the Velocity, I got 4.82m/s. so that becomes the new velocity I have and the New initial velocity would be 0. My New givens are:

Vi = 4.82m/s
Vf = 0m/s
A = -9.81m/s^2
[tex]\Delta[/tex]y = ?

If I'm looking for the change in height, I don't feel like I need Centripetal Force. Would I just need to worry about [tex]\Delta[/tex]y? or do I have to use the Centripetal force equation?
 
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  • #2
KEib + KEfb = KEia + KEfa

and what about PE ??:wink:
 
  • #3
Oh! Haha I completely forgot. Thanks so much!
 

Related to Circular Motion: Change in Height, Box Struck by Arrow

1. What is circular motion?

Circular motion refers to the movement of an object along a circular path. This means that the object is constantly changing its direction while maintaining a constant speed.

2. How does an object's height change during circular motion?

In circular motion, an object's height changes as it moves along the circular path. This is because the object is constantly moving towards and away from the center of the circle, resulting in changes in its vertical position.

3. How does circular motion affect an object when it is struck by an arrow?

When an object is struck by an arrow while in circular motion, its direction and velocity will change depending on the angle at which the arrow hits. The object will also experience a change in height, as it is being pushed in a different direction by the force of the arrow.

4. What factors can affect the change in height of an object in circular motion?

The change in height of an object in circular motion can be affected by the speed of the object, the size and shape of the circular path, and the force acting upon the object. If the object is in a vacuum, it will not experience any change in height due to air resistance.

5. How does the force of gravity affect an object in circular motion?

The force of gravity affects an object in circular motion by keeping it in its circular path. Without the force of gravity, the object would move in a straight line instead of a circular path. Gravity also plays a role in changing the height of the object during circular motion.

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