Calculations 5.1 Part 1. Determine effective coefficient of friction For each of the first four trials, calculate the change in linear momentum for the cart during the interval of time it took to pass between the two photo-gates. Assume the cart is traveling in the positive direction. Since you now know , use equation 5 to determine the net force acting on the cart as it moved along the track for each trial. Determine the mean and associated error in the mean for these four values. Repeat these calculations for the four trials with the cart moving in the other direction on the track, again, assuming the cart is travelling in the positive direction. Check to see if the two results agree with each other? Should they? Average these two mean values to determine the average frictional force acting on the cart. Determine an effective coefficient of friction between the cart and track. 5.2 Part 2. Collisions You have 10 collisions to consider. For each collision determine the momentum of each cart both before and after the collision and the total linear momentum of the system (remember, direction matters!) both before and after the collision. If a cart was initially at rest, its initial linear momentum is zero. List all these results, in tabular form, giving initial and final momentum of each cart, as well as the linear momentum of the system both before and after the collision. Construct a graph plotting the linear momentum of the system after the collision on the axis y and the linear momentum of the system before the collision on the axis. Determine the x equation of the best fit line for this graph. Compare the slope and intercept of your best fit y line with the values predicted by conservation of linear momentum. 5.3 Part 3. External impulse For each trial, calculate the change in velocity for the cart between the final time it passes through the photo-gate and the initial time it passes through the photo-gate. List these results, for each trial, in a table along with the impulse imparted to the cart by the spring, as determined by the area under the force curve. Construct a graph of Impulse imparted (as measured from your force graphs) vs change in velocity using the data from all trials. Using linear regression, determine the best fit straight line to this data. What should the slope and of this line be? If you what y-intercept don’t know the slope and should be, look at equation 5 for help. Compare your results with y-intercept these expected theoretical values. Are they in agreement?
Calculations 5.1 Part 1. Determine effective coefficient of friction For each of the first four trials, calculate the change in linear momentum for the cart during the interval of time it took to pass between the two photo-gates. Assume the cart is traveling in the positive direction. Since you now know , use equation 5 to determine the net force acting on the cart as it moved along the track for each trial. Determine the mean and associated error in the mean for these four values. Repeat these calculations for the four trials with the cart moving in the other direction on the track, again, assuming the cart is travelling in the positive direction. Check to see if the two results agree with each other? Should they? Average these two mean values to determine the average frictional force acting on the cart. Determine an effective coefficient of friction between the cart and track. 5.2 Part 2. Collisions You have 10 collisions to consider. For each collision determine the momentum of each cart both before and after the collision and the total linear momentum of the system (remember, direction matters!) both before and after the collision. If a cart was initially at rest, its initial linear momentum is zero. List all these results, in tabular form, giving initial and final momentum of each cart, as well as the linear momentum of the system both before and after the collision. Construct a graph plotting the linear momentum of the system after the collision on the y axis and the linear momentum of the system before the collision on the x axis. Determine the equation of the best fit line for this graph. Compare the slope and y intercept of your best fit line with the values predicted by conservation of linear momentum. 5.3 Part 3. External impulse For each trial, calculate the change in velocity for the cart between the final time it passes through the photo-gate and the initial time it passes through the photo-gate. List these results, for each trial, in a table along with the impulse imparted to the cart by the spring, as determined by the area under the force curve. Construct a graph of Impulse imparted (as measured from your force graphs) vs change in velocity using the data from all trials. Using linear regression, determine the best fit straight line to this data. What should the slope and y-intercept of this line be? If you don’t know what the slope and y-intercept should be, look at equation 5 for help. Compare your results with these expected theoretical values. Are they in agreement?