Hooke's Law and the Simple Harmonic Motion of a Spring

Purpose: To determine the force of a spring and to study the motion of a spring and mass when vibrating under influence of gravity.

2. Make a plot of the downward force applied to the spring verses the displacement of the spring.

Spring vs. Displacement Graph

3. Create a table with data.

Data Table

Graph for m = 1050g

Conclusion: This lab was very difficult. We were supposed to use Hook's Law for this lab. I learned that the force and the displacement are inversely proportional. If one is increasing the other is decreasing. To make this lab better, it would be good to have learned Hook's Law first and then tried the lab. Some sources of error would be that the masses on the spring would get too close to the motion detector so it wouldn't read all of it.

The Ballistic Pendulum

Purpose: To use the ballistic pendulum to determine the initial velocity of a projectile using conservation of momentum and conservation of energy.
Part 1:

Ball shot into cylinder data

 5. From these data calculate the initial velocity v using equations V = (2gh)^1/2 and mv = (M+m)V.

mv = (M+m)(2gh)^1/2

v = [(M+m)(2gh)^1/2]/m

v = [(.1994+.0573)(2*9.8*.096)^.5]/.0573
v = 6.145 m/s

Part 2:

Ball shot not into cylinder data

2. From the values of deltaX and deltaY calculate Vo by the use of equations deltaX = Vox*t + .5ax*t^2 and deltaY = Voy*t + .5ay*t^2.

deltaX = 2.7319 and deltaY = -1.006

Vox = deltaX/(deltaY/-4.9)^.5

Vox = 2.7319/(-1.006/-4.9)^.5

Vox = 6.029

3. Find the percent difference

[(6.145 - 6.029)/6.029]*100 = 1.92% difference

Conclusion: This lab was to have us find velocity for a projectile object. I learned that it is best to have the same person launch the ball each time. Otherwise it is one more variable that isn't controlled. The error in our lab could have come from having different people launch the ball. To make this lab better we can keep as many things consistent as we can.

Inelastic Collisions

Purpose: To analyze the motion of two low friction carts during an inelastic collision and verify that the law of conservation of liner momentum is obeyed.

Mass bar 1: .497 kg
Mass bar 2: .495 kg
Cart 1: .501 kg
Cart 2: .517 kg

2. Does it provide a reasonable graph of the motion of the cart?
- The graph showed a reasonable graph for the motion of the cart closest to the detector and then again when the carts collided and stuck.

3. What should these graphs look like?
- The graphs of position vs. time should be increasing throughout the whole graph. At the point of collision, the slope is small that before the collision.

- It is a good approximation to get the velocity right before and after the collision if momentum is conserved. P of C1 proportional to P of C1 + C2.

Trials with different mass

5. The velocity vs. time graph is all constants at different values during certain time intervals. The acceleration vs. time graph is a constant zero for the entire graph.

7. For most of the trials we got around 20% difference. There was a few that we were about to get around 10% difference. In the final set of trials, we got one trail around 6% and another at just under 4%. The law was obeyed fairly well. We could have done better. However, there are sources of error to take into account.

Kinetic energy lost

8. Kinetic energy = .5mv^2











9a) A mass, m, colliding with an identical mass, m, initially at rest.

deltaK/Ki = (Kf-Ki)/Ki = Kf/Ki - 1

9b) A mass, 2m, colliding with a mass, m, initially at rest.

 deltaK/Ki = (Kf-Ki)/Ki = Kf/Ki - 1 

Kf/Ki - 1  = .5(2m)Vf^2/.5mVi - 1 = 2Vf^2/Vi - 1

Vf = Vi/2

2Vf^2/Vi - 1 = 2(Vi/2)/Vi - 1 = -.5

9c) A mass, m, colliding with a mass, 2m, initially at rest.

deltaK/Ki = (Kf-Ki)/Ki = Kf/Ki - 1 

Kf/Ki - 1  = .5(m)Vf^2/.5(2m)Vi - 1 = Vf^2/2Vi - 1

Vf = Vi/2

Vf^2/2Vi - 1 = (Vi/2)/2Vi -1 = -.75

Conclusion: In this lab we learned about inelastic collisions and conservation of momentum. I learned about the kinetic energy and how to find the loss of kinetic energy when there is a collision. One source of error would be friction. We did not take into account the friction on the track. Also, depending on where the war was in relation to the motion detector, it may not have read it. The closer the carts get to the motion detector the harder it is to read it. To make this lab better, we would have to do more trials. Also, do all the calculations right after the trials so that we can use the best results.