If you were in a rotor style ride and the riders accelerate until the speed of ride is reached- if the radius of the cylinder is 5.0m and the coefficient of friction between clothes and wall is 0.5, how do you find minimum speed you would need to stick to the wall of the ride?
Could you explain how to set it thank you
you need a centripetal acceleration equal to 2g if the mu is 1/2
Force down = m g
friction force up = mu m v^2/r
g = mu v^2/r
v^2/r = g/mu = 2 g
v^2 = 2 r g
A 50KG BLOCK IS BEING PULLED BY A 200N FORCE ON A HORIZONTAL ROUH SURFACE AS SHOWN IN THE DIAGRAM.IF THE COEFFICIENT OF KINETIC FRICTION BETWEEN THE BLOCK AND THE SURFACE IS 0.3, FIND THE ACCELERATION OF THE BLOCK.
To find the minimum speed required to stick to the wall of the ride, we need to consider the forces acting on a rider in this situation. The key force is the friction force between the rider's clothes and the wall.
Here's how you can set up the problem:
1. Identify the forces: The two main forces at play are the gravitational force (mg) and the friction force (μN), where μ is the coefficient of friction and N is the normal force.
- Gravitational force (mg) is acting downward towards the center of the ride.
- Friction force (μN) is acting towards the center of the ride, pointing opposite to the gravitational force.
2. Determine the normal force: The normal force is the force exerted by the wall perpendicular to the surface. In this case, it is equal to the gravitational force (mg) because the rider is not accelerating vertically.
3. Set up the equation for forces in the radial direction: In circular motion, the net force in the radial direction is equal to the centripetal force required to maintain the circular motion.
- Net force = Friction force (μN)
- Centripetal force = (mass of the rider) × (centripetal acceleration)
4. Calculate the centripetal force: Centripetal force is given by the formula: Centripetal force = (mass of the rider) × (velocity^2 / radius). Therefore, the centripetal acceleration is given by: Centripetal acceleration = (velocity^2 / radius)
5. Equate the net force and centripetal force: Set the friction force (μN) equal to the centripetal force.
6. Solve for velocity: Substitute the expression for the centripetal acceleration into the equation, and solve for velocity. Remember that the normal force (N) is equal to the gravitational force (mg).
The minimum velocity required to stick to the wall can be found using the above steps. Plug in the given values for the radius (5.0 m) and the coefficient of friction (0.5), and solve for the velocity.