1. Dynamics Circular Motion, Part 2

2. Example 1
A 200 g mass is attached to one end of a string of length 80 cm. The other end of the string is tied to a fixed point on the ceiling. The apparatus is set into motion so that the mass moves in a circular path and the string traces out a cone,  = 30o.
a. Complete a FBD for the mass in the position shown. θ  T Fg T Fg

3. Example 1
A 200 g mass is attached to one end of a string of length 80 cm. The other end of the string is tied to a fixed point on the ceiling. The apparatus is set into motion so that the mass moves in a circular path and the string traces out a cone,  = 30o.
b. Determine the tension in the string. θ 
Split tension into components.
The mass does not move up or down, so Tx Ty T Fg

4. Example 1
A 200 g mass is attached to one end of a string of length 80 cm. The other end of the string is tied to a fixed point on the ceiling. The apparatus is set into motion so that the mass moves in a circular path and the string traces out a cone,  = 30o.
c. Determine the tangential speed of the mass.
Tx points to the center θ  Tx Ty T Fg
Need to solve for the radius

5. Example 2
Another type of conical pendulum. The masses are attached to each other by a string, that passes through a tube. Mass m1 = 0.6 kg is spun in a circle of radius r = 60 cm at a speed sufficient to keep mass m2 = 1.0 kg stationary.
a. Complete FBD’s for each mass in the positions shown in the diagram. m2 m1 T
Fg1 T
Fg2 m1 m2

6. Example 2
Another type of conical pendulum. The masses are attached to each other by a string, that passes through a tube. Mass m1 = 0.6 kg is spun in a circle of radius r = 60 cm at a speed sufficient to keep mass m2 = 1.0 kg stationary.
b. Determine the centripetal force.
Split T into components
Tx points to the center m2 m1
Fg2
Fg1 T Tx Ty
m1 and m2 don’t move up or down

7. Example 2
Another type of conical pendulum. The masses are attached to each other by a string, that passes through a tube. Mass m1 = 0.6 kg is spun in a circle of radius r = 60 cm at a speed sufficient to keep mass m2 = 1.0 kg stationary.
c. Determine the tangential velocity
From the previous slide m2 m1
Fg2
Fg1 T Tx Ty

8. Example 3
The gravitron is a common amusement park ride, where the room spins so fast that occupants feel pressed against the wall. When a sufficient speed is reached the floor drops down, but the occupants do not slide down the wall.
a. Complete the FBD for the rider in the position shown.
Add the invisible force first f
What is holding the rider in (keeping him from shooting out of the room) ? N
What is keeping him from sliding down the wall? Fg

9. Example 3
The gravitron is a common amusement park ride, where the room spins so fast that occupants feel pressed against the wall. When a sufficient speed is reached the floor drops down, but the occupants do not slide down the wall.
The normal force is pointing toward the center of the circle
If the rider does not move up or down, then Fg f N