The flywheel of a motor is connected to the flywheel of an electric generator by a drive belt. The flywheels are of equal size each of radius . While the flywheels are rotating the tension in the upper and lower portions of the drive belt are and respectively. The drive belt exerts a torque on the generator (around its center). The coefficient of static friction between the drive belt and each flywheel is . Assume the tension is as high as possible with no slipping between the belt and the flywheel, and that the drive belt is massless.
(a) Derive a differential expression representing the change of tension along the portion of the belt in contact with one of the flywheels. That is find the value of for one of the two flywheels.
(b) What is T1,T2
I am not sure about (a) I think it is us*d(theta).
(b)T/R 1/e^(us*pi)-1
(c)T/R 1/1-e^(-us*pi)
I am not 100% positive. Take a look maybe you feel the same way. The tension is opposite.
i check them they are ok thx a lot..
To derive the differential expression representing the change of tension along one portion of the belt in contact with one of the flywheels, we can use the principles of static friction. Here's how you can do it:
(a) Start by considering a small section of the drive belt in contact with one of the flywheels. Let's call the length of this section "dl".
The tension in the upper portion of the belt can be approximated as T + dT1, where T is the tension at the initial point of the section, and dT1 is the change in tension over the length dl.
Similarly, the tension in the lower portion of the belt can be approximated as T - dT2, where dT2 is the change in tension over the length dl.
The net torque exerted on the generator by the drive belt is given by the difference in torques between the tension in the upper portion and the tension in the lower portion.
The torque due to the tension in the upper portion is (T + dT1) * r, where r is the radius of the flywheel.
The torque due to the tension in the lower portion is (T - dT2) * r.
Since there is no slipping between the belt and the flywheel, the torques must balance each other, so we have:
(T + dT1) * r - (T - dT2) * r = 0
Expanding this equation gives:
r * dT1 - r * dT2 = 0
Dividing both sides by r, we get:
dT1 - dT2 = 0
Rearranging the equation, we find:
dT1 = dT2
This tells us that the change in tension on one side of the flywheel (dT1) is equal to the change in tension on the other side (dT2).
(b) T1 and T2 refer to the tensions in the upper and lower portions of the belt respectively. The values of T1 and T2 cannot be determined from the given information and will depend on various factors such as the rotational speed of the flywheels and the specific motor and generator being used.