The work done against friction reduces the amount of energy available for transformation into other forms. This is a significant way in which real systems are “open.” This investigation explores friction in a typical braking situation in which work done against friction reduces kinetic energy.
Part 1: Rolling friction
Open the 10D_FrictionAndLosses experiment file in your software, and then connect your Smart Cart using Bluetooth.
Set the cart on a level surface. Start data collection, and then give the cart a gentle push.
Observe the cart’s position, velocity, and acceleration graphs as the cart is pushed and as it rolls freely to a stop.
Write an equation expressing conservation of energy for the cart as it rolls to a stop.
Solve the equation for the coefficient of rolling friction μr.
Calculate μr using your equation, and the data from your position and velocity graphs.
Part 2: Kinetic friction
Attach a friction block to the plunger-end of the Smart Cart with a short string.
Record data as you give the cart a push, pulling the friction block behind it. There should be no slack in the string when you push.
Observe the graphs for the motion of the cart and friction block as they freely come to rest.
Draw separate free-body diagrams representing the cart and friction block as they slow down.
Write a conservation of energy equation that includes the kinetic energy of the cart and friction block and the work done by friction at the start and end of the sliding motion.
Solve the equation for the coefficient of sliding friction μk.
Calculate μk using the measured masses and data from your graphs.
Create an equation model to predict the stopping distance.
Add mass to the friction block, and then predict the stopping distance.
Test your prediction with the cart using the same initial velocity as before.
Explain any differences between your prediction and measurement.
Part 3: Combining the two
Move the mass to the cart and reattach the friction block with 1/2 m of string. Arrange for the cart and block to roll freely before starting to move the block.
Observe the graphs as the cart is pushed, rolls freely, catches the friction block, and drags it until both come to rest.
Sketch a copy of your velocity graph and identify where on the graph (i) positive work is done on the cart and (ii) the cart does positive work on its environment (the friction block and surface).