1. Dynamics III
Friction and Inclines

2. FBD

3. Example
A box with a mass of 60.0kg is being pulled by two forces as show below. Find the net acceleration of the box. Which way is the box moving?
12.0 N
θ = 30.0°

4. What will the scale read if the elevator is at rest?
Snowman mass = 50 kg, Scale Reading is Normal Force N mg
????????
490 (N)

5. What will the scale read if the elevator has
an upward acceleration of 2 m/s2 ?
Snowman mass = 50 kg
(he doesn’t melt) N mg
????????
590 (N)
Scale reads 590(N) increasing speed on the way up OR decreasing speed on the way down

6. What will the scale read if the elevator is
moving at a constant velocity?
Snowman mass = 50 kg N mg
????????
490 (N)
Scale reads 490(N) for constant velocity on the way up or way down (and when at rest)

7. What will the scale read if the elevator has
a downward acceleration of 3 m/s2 ?
Snowman mass = 50 kg N mg
????????
340 (N)
Scale reads 340(N) increasing speed on the way down OR decreasing speed on the way up

8. What will the scale read if the elevator has
a downward acceleration of 9.8 m/s2 ?
Snowman mass = 50 kg N mg
????????
0 (N)
Scale reads 0(N) increasing speed on the way down OR decreasing speed on the way up

10. Friction Force
Friction force is caused by surfaces sliding over each other
Symbol: Ff
Direction: Opposite to the motion of the object
Magnitude: If object is sliding,
𝐹 𝑓 = 𝜇 𝑘 𝐹 𝑛
where 𝜇 𝑘 = coefficient of kinetic friction
Magnitude: if object is not sliding
𝐹 𝑓 = 𝜇 𝑠 𝐹 𝑛
where 𝜇 𝑠 = coefficient of static friction

11. Example
A box of books is being dragged across the ground ( = 0.81) by a rope (FA = 170 N, 33 from horizontal). If m = 15 kg, calculate ax.
Fx = FAcos  Ff = max
ax = (FAcos  Ff)
We would be done except we don’t know Ff
How do we get Ff?
m = 15 kg
ax = ?
FA = 170 N 
 = 33
 = 0.81 FA Fg FN Ff m

12. FBD on an incline