How is the work done on a system related to its change in energy?
How is the efficiency of a system calculated?
In this investigation you will explore the relationship between work and kinetic energy by measuring the work done on a cart to accelerate it, and then comparing that work to the cart’s change in kinetic energy.
Part 1: Work and kinetic energy when force is constant
Set up the equipment like the picture. Open the
experiment file 10B_WorkEnergyTheorem, and connect to the Smart Cart with Bluetooth.
Unhook the thread from the cart. Measure the mass of cart and two 250‑g masses.
Zero the cart's force sensor while nothing is touching the hook.
Reattach the thread, and then roll the cart all the way to the end of the track opposite the pulley and hold it in place. Start recording data and release the cart.
Catch the cart before it hits the pulley. Data collection automatically stops after 1.5 s.
Use your data to determine the net work Wnet done on the cart (Wnet = area under your force versus position data), and the final speed of the cart vf. Record both values in a table.
Part 2: Work and kinetic energy when force is not constant
Unhook the hanging mass and have a group member hold the loose end of the thread in their hand at the other end of the track (no tension in the thread). Zero the force sensor.
Start recording data, and then gently pull on the string so the cart rolls down the track. Catch the cart before it rolls into the pulley.
Use your data to determine, and record, the work done on the cart, and the cart’s final speed.
Use the work-energy theorem to derive an equation for the final speed of the cart vf in terms of mass m and net work Wnet. Assume the initial speed of the cart is zero. Show your work.
Use the equation you derived and your measured value for Wnet. Calculate and record the theoretical final speed of the cart for Part 1 and Part 2.
How does the theoretical final speed of the cart compare the experimental (measured) value in both parts? If the values are different, what do you think caused the difference?
How efficient was the work done to change the cart’s kinetic energy in each part? Explain the significance of the values you obtain. (Efficiency = ΔEk /Wnet × 100%)
If you do 0.621 N∙m of work on a cart (same mass as the cart in this experiment) to accelerate it from rest, what would the cart’s final speed be if the efficiency of the work was 90.3%?
You may find this interactive equation useful in this investigation.
This interactive equation calculates the conservation of energy for a falling ball that has an initial velocity of zero.