Newton's second law
Under the same pull, a heavier cart accelerates more slowly.
Acceleration is proportional to the net force and inversely proportional to mass. Balance friction before measuring: remove the hanging mass, raise the end of the board away from the pulley, and give the cart a gentle push until the dots on the tape are evenly spaced. The component of gravity along the board, Mg sin θ, then exactly cancels the resistance μMg cos θ. Next, adjust the pulley height so that the string is parallel to the board; only then does the whole pull act along the board, so the net force on the cart equals the string tension. The experiment uses the weight mg of the hanging mass in place of the tension, but the true tension T = Mmg / (M + m) is always less than mg; the two are nearly equal only when the hanging mass is much smaller than the cart's mass.
Speed after a gentle push vs. time
A flat line (uniform motion) means friction is balanced; sloping down means under-balanced, sloping up means over-balanced.
Think about it
Once friction is balanced, do you need to balance it again after adding weights to the cart?
No. At balance Mg sin θ = μMg cos θ, i.e. tan θ = μ, which does not depend on the cart's mass: after balancing in step ①, change M and the dots stay evenly spaced. Also keep the hanging mass much smaller than the cart's mass, because using mg in place of the tension makes the relative error in acceleration exactly m/M.
Model assumptionsTrack 1 m long · μ includes friction and tape drag · maximum static friction equals kinetic friction · push speed 0.4 m/s · one counting point every 0.1 s · pulley mass ignored
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.