Motion in 2D and Pulleys

1
Motion in 2D and Pulleys

• Constant acceleration in 2-D
• Free fall in 2-D
• Talk about CAPA 16 21

2
Example Problem Cannon on a slope.
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 ?
3
Atwoods Machine
Calculate the acceleration of the blocks.
Assume - no friction - massless rope and
pulley - rope doesnt stretch
Plan free-body diagram for each mass
relate tensions, accelerations use Newtons
second Law
m2
m1
4
Forces on m2
Forces on m1
T1
T2
a2
a1
m2g
m1g

• Tensions are equal (ideal pulley, light rope)
• Accelerations are equal in magnitude (why?),
  opposite in direction

5
m1g
. . .
is proportional to g, but can be small (and easy
to measure)
6
A block of mass m1 on a rough horizontal surface
is pulled with a force FA at an angle ? 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
Hint direction of friction on m1 depends on
direction of motion!