Velocity from Kinetic energy and work energy theorem

In summary, an arrow with a mass of 0.066 kg is fired horizontally with a force of 50 N over a distance of 0.95 m. The Work Energy Theorem can be used to calculate the change in kinetic energy of the arrow, which can then be used to find the final velocity. However, a mistake in the algebra used to solve for the final velocity resulted in an incorrect answer of 0 m/s. The correct equation for the final velocity is the square root of (2 * 0.066 kg * 50 N * 0.95 m)/(0.066 kg), which gives a final velocity of approximately 6.84 m/s. The work done on the arrow can also be calculated
  • #1
IAmSparticus
36
0
1. A 0.066 kg arrow is fired horizontally. The bowstring exerts an average force of 50 N on the arrow over a distance of 0.95 m. With what speed does the arrow leave the bow?


2. Work Energy Theorem = change in kinetic energy = (1/2*mass*Final Velocity^2)-(1/2*mass*Initial Velocity^2)



3. Since the initial speed is zero and the mass is given, I get a solution of 0, but that is most likely because I did the algebra wrong. I got an equation of Final Velocity = Square root (2*.066kg*0m/s)/(2*.066)

Which is clearly wrong. Where did I go wrong?
 
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  • #2
What is the work done on the arrow?
Equate it to the kinetic energy of the arrow and find the velocity.
 
  • #3



1. To calculate the velocity of the arrow, we can use the work-energy theorem, which states that the change in kinetic energy of an object is equal to the work done on the object. In this case, the work done on the arrow by the bowstring is equal to the change in kinetic energy of the arrow. Therefore, we can set up the equation as follows:

Work done = Change in kinetic energy

50 N * 0.95 m = 1/2 * 0.066 kg * (final velocity)^2 - 1/2 * 0.066 kg * (0 m/s)^2

47.5 J = 0.033 J - 0

47.5 J = 0.033 J

Therefore, the final velocity of the arrow is √(47.5/0.033) = 57.5 m/s.

2. The work-energy theorem is a useful tool for calculating the velocity of an object, but it is important to note that it only applies to situations where the net work done on an object is equal to the change in kinetic energy. In this case, the initial velocity of the arrow is zero, so the work-energy theorem can be used. However, if there is an initial velocity, we would need to use a different equation, such as the equation for conservation of energy, to calculate the final velocity.

3. In your calculation, you have correctly set up the equation for the work-energy theorem, but you have made a mistake in the algebra. The correct equation should be:

Final Velocity = √(2*47.5 J/0.066 kg) = √(2*719.7 m^2/s^2) = 57.5 m/s

It appears that you have mistakenly used the mass of the arrow instead of the work done on the arrow in the equation. It is important to be careful with units when using equations to ensure accurate calculations.
 

1. What is the relationship between velocity and kinetic energy?

The relationship between velocity and kinetic energy is that as velocity increases, kinetic energy also increases. This means that the faster an object is moving, the more kinetic energy it has.

2. How is velocity calculated from kinetic energy?

Velocity can be calculated from kinetic energy by using the formula v = √(2KE/m), where v is velocity, KE is kinetic energy, and m is the mass of the object.

3. How does the work energy theorem relate to velocity?

The work energy theorem states that the work done on an object is equal to the change in its kinetic energy. This means that if work is done on an object, its velocity will change accordingly.

4. Can the work energy theorem be used to calculate velocity?

Yes, the work energy theorem can be used to calculate velocity by rearranging the formula to v = √(2W/m), where v is velocity, W is the work done on the object, and m is the mass of the object.

5. How does mass affect the velocity of an object in relation to kinetic energy?

The mass of an object affects its velocity in relation to kinetic energy by directly influencing the amount of kinetic energy the object possesses. The greater the mass, the more kinetic energy is required to achieve a certain velocity.

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