Purpose: To Prove the law of conservation of energy, by showing that the initial potential energy of a falling mass will be converted to an equal amount of kinetic energy plus the work done by friction.

1. Record the mass of the dynamics cart (m = 0.5 kg) in your data table.
2. Place the cart near the top of the incline; note this position so that all of you drops can be made from the same position. Place the photo-gate near the bottom of the incline and note its position as well.
   
1. Measure the height from center of the cart to the top of the table. Label this h_1.
2. With the cart in the middle of the photo-gate measure the height from the center of the cart to the top of the table. Label this h₂.
3. To determine the height the cart will fall during its run, calculate the difference between h₁ and h₂. Record this value as h. (h = h₁ – h₂).
3. Calculate the potential energy of the cart. (U)
4. Measure the distance (d) the cart will travel along the ramp from its starting position to the photo-gate.
5. Use the values of h and d to calculate the angle (q) the ramp is inclined.
6. Calculate the parallel and perpendicular components of the cart’s weight.
7. Calculate the theoretical kinetic energy (K_T) the cart will acquire when it reaches the bottom of the ramp by the following formula (K_T = W_||d). This is the kinetic energy the cart would acquire in the absence of friction.
8. Calculate the cart’s theoretical velocity (v_T). This is the speed the cart would acquire at the bottom of the ramp in the absence of friction.
9. Use the smart timer and photo-gate to measure the real velocity (v_m) of the cart. This velocity should be smaller than the velocity in #8 because of the presence of friction.
10. Calculate the real measured value of kinetic energy (K_m). Again this should less than #7 due to the presence of friction.
11. Friction
   
1. Calculate the Work don by friction (W_f). This is determine by finding the difference between the real kinetic energy and the theoretical kinetic energy, because the work that friction does is the difference between these two values.
2. Calculate the force of friction (f). W_f = fd
3. Calculate the coefficient of friction (m).
12. Add K_m and W_f and compare the result to U. They should be very close. Calculate the percent error using the following formula. %Error = |(K_m + W_f) – U| / U

All data is to be recorded in a table, show all calculations

Was the purpose achieved?

If so explain how, if not explain why?