Finding Apparent Weight with Uniform Circular Motion

In summary, a ferris wheel with a radius of 14.0 m rotates at a constant rate, completing three revolutions in 50.0 s. The apparent weight of a 60.0 kg passenger when she is at the top of the wheel is 469 N. This is found by using the equations T=2∏/ω, a=(ω^2)r, and F=ma to calculate the angular velocity, centripetal acceleration, and force on the passenger. The weight is then determined by subtracting the force due to centripetal acceleration from the net force of gravity and acceleration.
  • #1
CalebtheCoward
8
0

Homework Statement



A ferris wheel with a radius of 14.0 m rotates at a constant rate, completing three revolutions in 50.0 s. What is the apparent weight of a 60.0 kg passenger when she is at the top of the wheel?
Given choices: 532 N, 452 N, 562 N, 625 N, 469 N

Homework Equations



T=2∏/ω, a=(ω^2)r, F=ma

The Attempt at a Solution



3 rev/ 50 s = 0.37 (rad/s)
a=1.92 (m/s^2)
F=(a+g)m=(1.92+9.81 (m/s^2))(60.0 kg)=703.8 N
 
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  • #2
Your attempt is a bit incomplete. You are forgetting to include the force due to centripetal accelaration which is
2R
Find it and subtract it from the value u got in ur attempt
The force equation on the man is
m(g+a)-mω2r
 
  • #3
Firstly we should be clear about definition of weight ,as per halliday "The weight W of a body is the magnitude of the net force required to prevent the body from falling freely, as measured by someone on the ground"..Now what you have found in your attempt is weight at the lowest point on the wheel.At the topmost point it should be M(g-ω^2r)..think it like a body in an elevator moving downwards at acceleration of magnitude ω^2r. Mathematically you can remember weight as M(⃗g-⃗a). so at lowermost position ⃗g-⃗a will come out to be 9.8+ω^2r and at top 9.8-ω^2r. For this particular question answer is 469 N.
 

Related to Finding Apparent Weight with Uniform Circular Motion

1. What is apparent weight in uniform circular motion?

Apparent weight in uniform circular motion is the perceived weight of an object moving in a circular path. It is the combination of the object's actual weight and the centrifugal force acting on the object due to its circular motion.

2. How do you calculate the apparent weight in uniform circular motion?

The formula for calculating the apparent weight in uniform circular motion is: Apparent weight = Actual weight - Centrifugal force. The centrifugal force can be calculated using the formula: Centrifugal force = (Mass x Velocity^2) / Radius.

3. What factors affect the apparent weight in uniform circular motion?

The apparent weight in uniform circular motion is affected by the mass of the object, the velocity of the object, and the radius of the circular path. The greater the mass and velocity, and the smaller the radius, the greater the apparent weight will be.

4. How does the apparent weight change as the object moves in a circular path?

As the object moves in a circular path, the apparent weight changes due to the changing direction of the velocity. At the top of the circular path, where the velocity is horizontal, the apparent weight will be equal to the actual weight. As the object moves down the circular path, the apparent weight will decrease due to the centrifugal force pulling the object away from the center of the circle.

5. Why is it important to consider apparent weight in uniform circular motion?

It is important to consider apparent weight in uniform circular motion because it affects the perceived weight of an object and can have implications in various situations such as amusement park rides, satellite orbits, and even sports like gymnastics. Understanding the concept of apparent weight can help ensure the safety and accuracy of these activities.

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