Calculating the Speed of a Ball Shot from a Spring Gun

In summary, a spring gun with a spring constant of 28 N/m is used to shoot a 56-g ball horizontally. The spring is initially compressed by 18 cm and the ball leaves the gun when the spring is compressed by 12 cm. To calculate the speed of the ball when it hits the ground 1.4 m below the gun, you need to consider the energy from the spring and the gravitational potential energy. After converting these energies into kinetic energy, you can solve for the final velocity. Remember to check your units to ensure an accurate calculation.
  • #1
cstout
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Homework Statement


A spring gun (k = 28 N/m) is used to shoot a 56-g ball horizontally. Initially the spring is compressed by 18 cm. The ball loses contact with the spring and leaves the gun when the spring is still compressed by 12 cm. What is the speed of the ball when it hits the ground, 1.4 m below the spring gun?


Homework Equations



horizontal velocity, vertical velocity, Kinetic energy
 
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  • #2
Assuming no energy is lost to friction you have two sources of energy.
1, The energy from the spring = force * distance.
2, The gravitational energy of falling the 1.4m = m g h

Both of these will be converted into kinetic energy of the particle = 1/2 m v^2
from this you can get the final speed.
 
  • #3
is the distance the change in the compression of the spring for the energy of the spring?
 
  • #4
Yes - the energy stored in a spring is 1/2 K x^2
where K is the spring constant and X is the distance you compress it.
 
  • #5
i got .0504 for the spring energy and 768.32 for the gravitational potential energy.
but then what equation or steps do i use to convert those into kinetic energy to get the final velocity
 
  • #6
Check your units!
You just add the spring energy and potential energy to get the kinetic energy.
 

1. How do you calculate the speed of a ball shot from a spring gun?

The speed of a ball shot from a spring gun can be calculated by using the formula v = √(2k/m), where v is the velocity of the ball, k is the spring constant, and m is the mass of the ball. This equation is derived from the conservation of energy principle, where the potential energy stored in the spring is converted into kinetic energy of the ball.

2. What is the spring constant and how is it determined?

The spring constant, denoted by k, is a measure of the stiffness of the spring. It represents the amount of force required to stretch or compress the spring by one unit of length. The value of k can be determined experimentally by measuring the force applied to the spring and the resulting displacement.

3. Can the speed of the ball be affected by factors other than the spring constant and mass?

Yes, the speed of the ball can also be affected by external factors such as air resistance, friction, and the angle at which the ball is shot. These factors can cause a decrease in the speed of the ball compared to the calculated value.

4. How accurate is the calculated speed compared to the actual speed of the ball?

The calculated speed of the ball is an ideal value and may differ from the actual speed due to external factors and the assumptions made in the calculation. However, it can provide a good estimate and can be improved by using more precise measurements and taking into account other influencing factors.

5. Are there any safety precautions that should be taken when conducting experiments with a spring gun?

Yes, it is important to follow safety precautions when working with a spring gun. Make sure the gun is pointed in a safe direction and always wear protective gear, such as goggles, when shooting the ball. Also, do not aim the gun at people or animals and make sure to use appropriate force and mass values to prevent any potential hazards.

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