Discover the Tangential Velocity for the Wall of Death Amusement Park Ride

In summary, the Wall of Death is a ride in an amusement park where riders stand against a spinning vertical cylinder and are held up by friction. To find the tangential velocity necessary for riders to not slip down the wall, one must first calculate the centripetal acceleration using the given coefficient of static friction and radius of the cylinder. Then, the relationship between the frictional force and normal reaction must be understood in order to write the correct equation for minimum tangential velocity.
  • #1
am08
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The Wall of Death in an amusement park is comprised of a vertical cylinder that can spin around the vertical axis. Riders stand against the wall of the spinning cylinder and the floor falls away leaving the riders held up by friction. The radius of the cylinder is 3.9 m and the coefficent of static friction between the rider and the wall is 0.35. Find the tangential velocity of the spinning wall necessary so that the riders do not slip down the wall.

Centripetal Acc = (.35*9.8) = 3.43 m/s^2

How do I apply that to find the tangential velocity?
 
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  • #2
am08 said:
Centripetal Acc = (.35*9.8) = 3.43 m/s^2

How did you get this??

Centripetal force is the normal reaction N. The frictional force F must be equal to weight. You should know the relationship between F and N when static friction is max. Now write the correct eqn for minimum tangential velocity.
 
  • #3


To find the tangential velocity, you can use the formula v = √(r*ac), where v is the tangential velocity, r is the radius of the cylinder, and ac is the centripetal acceleration. Plugging in the values given, we get:

v = √(3.9*3.43) = 4.56 m/s

Therefore, the tangential velocity of the spinning wall should be 4.56 m/s in order for the riders to not slip down the wall.
 

FAQ: Discover the Tangential Velocity for the Wall of Death Amusement Park Ride

1. What is tangential velocity?

Tangential velocity is the speed at which an object moves along a curved path, such as the circular path of the Wall of Death amusement park ride. It is the component of velocity that is parallel to the direction of motion.

2. How is tangential velocity calculated?

Tangential velocity can be calculated by dividing the distance traveled along the curved path by the time it takes to travel that distance. It can also be calculated by multiplying the angular velocity (in radians per second) by the radius of the circular path.

3. What factors affect the tangential velocity on the Wall of Death ride?

The tangential velocity on the Wall of Death ride is affected by the radius of the circular path, the angular velocity of the ride, and the mass of the rider. Additionally, any external forces, such as friction or air resistance, can also affect the tangential velocity.

4. Why is tangential velocity important for the Wall of Death ride?

Tangential velocity is important for the Wall of Death ride because it determines the speed at which the rider travels along the circular path. This speed, combined with the forces of gravity and centripetal force, creates the thrilling experience of the ride.

5. How can tangential velocity be increased on the Wall of Death ride?

Tangential velocity on the Wall of Death ride can be increased by increasing the radius of the circular path, increasing the angular velocity of the ride, or decreasing the mass of the rider. It is important to note that increasing the tangential velocity also increases the forces acting on the rider, so safety precautions must be taken.

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