A circular-motion addict of mass rides a Ferris wheel around in a vertical circle of radius at a constant speed of. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b) the highest point of the circular path and (c) the lowest point?
The period of the motion is.
The magnitude of the normal force on the addict from the seat when both go through the highest point of the circular path is
The magnitude of the normal force on the addict from the seat when both go through the lowest point is.
This problem is based on the concept of uniform circular motion. Uniform circular motion is a motion in which an object moves in a circular path with constant velocity. Also, it involves Newton’s second law of motion.
The velocity in uniform circular motion is given by,
where, v is the velocity, R is the radius and T is the time period
According to Newton’s second law of motion
where, is an acceleration, g is an acceleration due to gravity, m is mass, is the normal force and R is the radius.
Using equation (i) the time can be written as,
Hence, the period of the motion is 10 s.
In this case, Normal force is directed upward, gravitational force mg is to downward and acceleration is also directed to the down. Thus, by using Newton’s 2nd law,
(Centripetal acceleration is due to the circular motion)
Hence, the magnitude of the normal force on the addict from the seat when both go through the highest point of the circular path is.
Now, reverse both the normal force direction and the acceleration direction
Hence, the magnitude of the normal force on the addict from the seat when both go through the lowest point is
A 1.5 kg box is initially at rest on a horizontal surface when at t =0 a horizontal force (with t in seconds) is applied to the box. The acceleration of the box as a function of time t is given b role="math" localid="1660971208695" and: for t>2.8 s (a) what is the coefficient of static friction between the box and the surface? (b) What is the coefficient of kinetic friction between the box and the surface?
Figure 6-32 shows three crates being pushed over a concrete floor by a horizontal force of magnitude . The masses of the crates are , , and .The coefficient of kinetic friction between the floor and each of the crates is . (a) What is the magnitude of the force on crate 3 from crate 2? (b) If the crates then slide onto a polished floor, where the coefficient of kinetic friction is less than , is magnitude more than, less than, or the same as it was when the coefficient was ?
A sling-thrower puts a stone (0.250 kg). In the slings pouch (0.010 kg) and then begins to make the stone and pouch move in a vertical circle of radius 0.650 m. The cord between the pouch and the person’s hand has negligible mass and will break when the tension in the cord is 33.0 N more. Suppose the sling thrower could gradually increase the speed of the stone. (a) Will the breaking occur at the lowest point of the circle or at the highest point? (b) At what speed of the stone will that breaking occur?
An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is , and the circle’s radius is . At the top of the circle, what are the
(a) magnitude and
(b) direction (up or down) of the force on the car from the boom if the car’s speed is ?
What are (c) and
(d) the direction if ?
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