A) 140 degrees
First of all, we need to find the angular velocity of the Ferris wheel. We know that its period is
T = 32 s
So the angular velocity is

Assuming the wheel is moving at constant angular velocity, we can now calculate the angular displacement with respect to the initial position:

and substituting t = 75 seconds, we find

In degrees, it is

So, the new position is 140 degrees from the initial position at the top.
B) 2.7 m/s
The tangential speed, v, of a point at the egde of the wheel is given by

where we have

r = d/2 = (27 m)/2=13.5 m is the radius of the wheel
Substituting into the equation, we find

Answer:
Time, t = 0.015 seconds.
Explanation:
Given the following data;
Mass, m = 0.2kg
Force, F = 200N
Initial velocity, u = 40m/s
Final velocity, v = 25m/s
To find the time;
Ft = m(v - u)
Time, t = m(v - u)/f
Substituting into the equation, we have;
Time, t = 0.2(25 - 40)/200
Time, t = 0.2(-15)/200
Time, t = 3/200
Time, t = 0.015 seconds.
Note: We ignored the negative sign because time can't be negative.
Answer:
a) 0.147 N
b) 9.408 N
c) 9.261 N
Explanation:
The tension on the cord is the only force keeping the block in circular motion, thus representing the entirety of its centripetal force
. Plugging in values for initial and final states and we get answers for a and b. The work done by the person causes the centripetal force to increase, and thus is the difference between the final tension and the initial tension.
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