A loop-the-loop ride at an amusement park has a radius of 5 m. At the highest point, the rider moves at 8 m/s. At the lowest point the rider moves at 13 m/s. Find what you would feel like you weigh at those points. (This force represents the force of the seat against your rear end; its F(app) and it takes the place of Tension for the ball on the string.)
I don't understand. If I replace Tension in the following equation, I will have 2 unknowns:
(highest point): T+mg=(mv^2)/R
F(app)+mg=(mv^2)/R
(lowest point): T-mg=(mv^2)/R
F(app)-mg=(mv^2)/R
i agree with your result, but tension is not involved.
At the top of the loop, the seat force F PLUS the weight provides the centripetal acceleration, and
F = MV^2/R -Mg
At the bottom of the loop,
F = M V^2/R + M g
Forgive my ignorance, but how do I find the mass when I do not know the seat force?
OK, so they don't tell you the mass. All you can say in response is BY WHAT FACTOR the force exceeds your weight at the bottom or is less at the top of the arc.
At the top of the arc, V^2/R = 12.8 m/s^2
F = M (12.8 - 9.8) = M* 3 m/s^2.
This is 3/9.8 or 30.6% of the weight of the person
At the bottom of the arc, V^2/R = 33.8 m/s^2, and the seat force is 4.44 times the weight.
I followed up to this point:
F = M (12.8 - 9.8) = M* 3 m/s^2.
I do not understand why we must divide by g (9.8).
You are comparing actual forces exerted by the seat to the weight of the person, which is Mg. That invoves taking a ratio, Force/(M*g).
Since they don't tell you the person's mass, all you can calculate is force ratios
Thanks drwls!
To solve this problem, we first need to understand the concept of apparent weight. Apparent weight is the sensation of weight experienced by an object or person in a non-inertial frame of reference, such as when riding on a looping roller coaster. The apparent weight is the force felt by the rider in addition to their actual weight due to the acceleration of the ride.
Let's analyze the situation at the highest point first. At this point, the rider is moving at 8 m/s. The net force acting on the rider is the centripetal force, provided by the normal force of the seat, F(app), minus the force of gravity (mg).
Using the equation for centripetal force, we have:
F(app) - mg = (m * v^2) / R
Here, m is the mass of the rider, v is the velocity, and R is the radius of the loop. Since we don't know the mass of the rider, we can cancel it out by dividing both sides of the equation by m:
F(app)/m - g = v^2 / R
Now, let's analyze the situation at the lowest point. Here, the rider is moving at 13 m/s, and the equation becomes:
F(app) + mg = (m * v^2) / R
Dividing both sides of the equation by m:
F(app)/m + g = v^2 / R
We can see that the equation for the highest point and the equation for the lowest point have a similar structure, but with opposite signs for F(app)/m:
F(app)/m - g = v^2 / R (highest point)
F(app)/m + g = v^2 / R (lowest point)
Now we can solve for F(app)/m in each equation:
F(app)/m = v^2 / R + g (highest point)
F(app)/m = v^2 / R - g (lowest point)
As you can see, we now have two equations with F(app)/m as the only unknown. To find the magnitude of F(app)/m at each point, we substitute the given values of v, R, and g into each equation:
At the highest point: F(app)/m = (8^2 / 5) + 9.8
At the lowest point: F(app)/m = (13^2 / 5) - 9.8
Evaluating these equations will give you the magnitudes of F(app)/m at each point. The values will represent what you would feel like you weigh at those points, as they represent the force of the seat against your rear end.