The
Mass-Dependence of Friction
Part I, Theory
• In your notebook or
on a piece of scratch paper, draw free-body diagrams for a cart of mass
m moving up and down a slope. The friction f is measurable.
You should have two separate diagrams. Choose a coordinate system
with the x-axis parallel to and pointing down the slope and with the
y-axis perpendicular to the slope.
• Write out Newton’s Second Law for each of the two
directions for both situations. Use au for
acceleration when the
cart is moving up the slope and ad for when it is moving
down the
slope. N stands for the normal force. The angle of the
slope up from the horizontal is θ. Your equations should be
expressed in terms of m, g, f, N, au, ad, sin θ,
and cos θ.
• Solve one of the equilibrium equations for N.
Subtract one of the non-equilibrium equations from the other to solve
for f. It will depend on m, au, and ad.
(The
parameters that are
known or can be measured in
lab are m, g, au, ad, and θ.) Then
introduce f = μN and solve for μ.
• Observe which equations depend on mass and which
are independent of mass.
When you are satisfied with what you have predicted, open today's
worksheet and answer Questions 1-3. You may copy and paste the
provided label and arrows. Enlarge the drawing canvas if
necessary, and similarly, you might find it easier to position the
arrows if you undo object snapping by going to Drawing
Tools → Align → Grid Settings. Check with your lab
instructor to confirm that your free-body diagrams and equations are
correct. Then move on to Part II.
Back to the Overview
On to Part II
Worksheet
Index