Transcript Document

Motion in 2D and Pulleys
• Constant acceleration in 2-D
• Free fall in 2-D
• Talk about CAPA # 16 & 21
Physics 1D03 - Lecture 8
1
Example Problem: Cannon on a slope.
100 m/s
30°
20°
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
2
Atwood’s Machine
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
Physics 1D03 - Lecture 8
m2
3
Forces on m1
T1
Forces on m2
T2
a2
a1
m2g
m1g
•
•
Tensions are equal (“ideal” pulley, light rope)
Accelerations are equal in magnitude (why?), opposite in
direction
Physics 1D03 - Lecture 8
4
T
T
a
a
m2g
m1g
m1g  T  m1a
T  m2g  m2a
.
.
.
 m1  m2 
g
Eliminate T to get  a  
 m1  m2 

a is proportional to g, but can be small (and easy to measure)
Physics 1D03 - Lecture 8
5
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.
FA
Determine the acceleration of the system.
θ
m1
m2
Hint: direction of friction on m1 depends on direction of motion!
Physics 1D03 - Lecture 8
6