Inelastic Collision with Pendulum and Ball; finding force and work

In summary, the lab involved launching a ball from a spring-loaded cannon into a pendulum, representing a totally inelastic collision. The question asked was how much work was done in compressing the spring for the long-range case, and which law of conservation is used to answer it. The law of conservation of energy is used, where potential energy stored in the compressed spring is equal to the work done. The spring constant is needed to calculate this potential energy, which can be found using the mass and speed of the ball.
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rk21619
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Homework Statement


I did a lab today in Physics in which we launched ball from a spring loaded cannon directly into a pendulum that captured the ball, held it, and swung upwards with it (representing a totally inelastic collision). One question that confuses me:

> How much work did you do in joules in compressing the spring of the spring gun for the long-range case? Which law of conservation is your answer based upon?

Some additional information: the long-range case is where we fired the ball at it's maximum speed (which I've calculated to be 4.79 m/s^2.

Homework Equations


E = K + U = 0
initial momentum = final momentum
m(v_initial) = (m + M)(v_final)
K = (1/2)(m + M)v^2
U = (1/2)kx^2 [for the spring]

The Attempt at a Solution



I'm guessing the law of conservation to use here is for that of energy, in which K + U = 0, where K is kinetic and U is final energy. The system has all potential energy (no kinetic) when the spring is compressed, which is known as (1/2)kx^2, but I don't know k...

If any other information is needed, let me know. Thanks for the help!
 
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  • #2


Hi there,

Thank you for sharing your lab experience with us! It sounds like you had an interesting experiment with the spring-loaded cannon and pendulum.

To answer your question, let's first define the law of conservation of energy. This law states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this case, we can use the conservation of energy to determine the work done in compressing the spring.

As you mentioned, the system has all potential energy (no kinetic) when the spring is compressed. This potential energy is stored in the spring and can be calculated using the equation U = (1/2)kx^2, where k is the spring constant and x is the distance the spring is compressed.

To find the spring constant, we can use the information given in the problem. You mentioned that the maximum speed of the ball is 4.79 m/s^2. This is the kinetic energy of the ball after it has been launched from the spring. Using the equation K = (1/2)(m + M)v^2, we can solve for the sum of the masses (m + M). This will give us the total mass of the system (spring and ball) which we can then use to find the spring constant.

Once we have the spring constant, we can use it to calculate the potential energy of the compressed spring (U = (1/2)kx^2). This will give us the amount of energy stored in the spring, which is also the work done in compressing the spring.

I hope this helps! Let me know if you have any further questions or need clarification on anything. Good luck with your lab report!
 

1. How do you calculate the force in an inelastic collision between a pendulum and a ball?

The force in an inelastic collision can be calculated using the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. In this case, the momentum of the pendulum and the ball before the collision is equal to the momentum of the combined system after the collision. By rearranging the equation, we can calculate the force by dividing the change in momentum by the time of the collision.

2. What is meant by an inelastic collision?

An inelastic collision is a type of collision where there is a loss of kinetic energy during the collision. This means that the objects involved in the collision do not bounce off each other and stick together after colliding. In contrast, in an elastic collision, there is no loss of kinetic energy and the objects involved bounce off each other after colliding.

3. How can you determine the work done in an inelastic collision between a pendulum and a ball?

The work done in an inelastic collision can be determined by calculating the change in kinetic energy of the system. This can be calculated by subtracting the final kinetic energy from the initial kinetic energy. The work done is equal to the change in kinetic energy, as described by the work-energy theorem.

4. What factors can affect the force and work in an inelastic collision?

The force and work in an inelastic collision can be affected by factors such as the mass and velocity of the objects involved, the angle of collision, and the elasticity of the objects. In general, a higher mass and velocity result in a greater force and work, while a lower elasticity results in a lower force and work.

5. Can you use the equations for elastic collisions to calculate force and work in an inelastic collision?

No, the equations for elastic collisions cannot be used to calculate force and work in an inelastic collision. In an elastic collision, the objects involved bounce off each other and there is no loss of kinetic energy. In an inelastic collision, there is a loss of kinetic energy, so the equations for elastic collisions do not apply.

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