1. Motion in 2D and Pulleys Constant acceleration in 2-D Free fall in 2-D
Talk about CAPA # 16 & 21
Physics 1D03 - Lecture 8

2. Example Problem: Cannon on a slope.
20° d
30°
100 m/s
How long is the cannonball in the air, and how far from the cannon does it hit ? With what velocity does it hit the slope ?
Physics 1D03 - Lecture 8

3. Atwood’s Machine Assume : - no friction
Calculate the acceleration of the blocks.
Assume : - no friction
- massless rope and pulley
- rope doesn’t stretch
Plan: • free-body diagram for each mass
• relate tensions, accelerations
• use Newton’s second Law m1 m2
Physics 1D03 - Lecture 8

4. T1 T2 a2 a1 m2g m1g Forces on m1 Forces on m2
Tensions are equal (“ideal” pulley, light rope)
Accelerations are equal in magnitude (why?), opposite in direction
Physics 1D03 - Lecture 8

5. is proportional to g, but can be small (and easy to measure)
m2g a
m1g .
Eliminate T to get 
is proportional to g, but can be small (and easy to measure)
Physics 1D03 - Lecture 8

6. Hint: direction of friction on m1 depends on direction of motion!
A block of mass m1 on a rough horizontal surface is pulled with a force FA at an angle θ to the horizontal. A ball of mass m2 is connected to the other side, hanging over a lightweight frictionless pulley. The coefficient of friction is given by μk. Determine the acceleration of the system. FA m1 m2 θ
Hint: direction of friction on m1 depends on direction of motion!
Physics 1D03 - Lecture 8