This is a very confusing problem, I had never taken physics before and it is going to kill my GPA. can someone please help me solve this problem. I have a quiz coming up. Thanks for the help.
The flywheel of an old steam engine is a solid homogeneous metal disk of mass M = 137 kg and radius R = 90.1 cm. The engine rotates the wheel at 413 rpm. In an emergency, to bring the engine to a stop, the flywheel is disengaged from the engine and a brake pad is applied at the edge to provide a radially inward force F = 109 N.
a) If the coefficient of kinetic friction between the pad and the flywheel is μk = 0.353, how many revolutions does the flywheel make before coming to rest?
b) How long does it take for the flywheel to come to rest?
c) Calculate the work done by the torque during this time.
parameter:m-137kg r-0.901m coeff-0.353m normal force-109N angular velocity-413rpm=43.25rad/s Torque exerted by friction=moment of inertiaI*angular acceleration Ffr=0.353*109=38.48N I=1/2MR^2=0.5*137*0.901^2=55.61Kgm^2 38.48*0.901=55.61*angular acceleration angular acceleration=0.6235rad/s^2(caused by friction) 43.25^2=4*0.6235*3.14n n=1871/7.83=239revs b) t=w/0.6235=43.25/0.6235=69.4secs c)W=Ffr*R*w=38.48*0.901*43.25*69.4=1.04*10^5J
To solve this problem, we need to use the principles of physics related to rotational motion, specifically torque and work-energy theorem. Let's break it down step by step:
a) To find the number of revolutions the flywheel makes before coming to rest, we need to find the angular deceleration of the flywheel. From there, we can calculate the time it takes to stop and convert it into the number of revolutions.
First, let's calculate the moment of inertia (I) of the flywheel using the formula:
I = (1/2) * M * R^2
where M is the mass of the flywheel and R is its radius.
Given that M = 137 kg and R = 90.1 cm = 0.901 m, we can substitute these values into the formula to find I.
Next, we need to calculate the torque (τ) acting on the flywheel. The torque can be calculated using the formula:
τ = F * R
where F is the radial inward force applied by the brake pad and R is the radius of the flywheel.
Given that F = 109 N and R = 0.901 m, we can substitute these values into the formula to find τ.
Using Newton's second law for rotational motion, τ = I * α, where α is the angular acceleration. Rearranging this equation, we have α = τ / I.
With the known values of τ and I, we can substitute them into the formula to calculate α.
The angular deceleration (α) is related to angular velocity (ω) and time (t) through the equation α = ω / t, where ω is the initial angular velocity (in radians per second). In this case, the initial angular velocity can be determined from the given value of 413 rpm (revolutions per minute). Convert this value to radians per second by multiplying it by (2π / 60).
Finally, by rearranging the equation α = ω / t, we can solve for t:
t = ω / α.
Now that we have the value of t, we can convert it to the number of revolutions. Multiply it by the initial angular velocity in revolutions per second to get the answer.
b) To find the time it takes for the flywheel to come to rest, we already have the value of t from part a).
c) To calculate the work done by the torque during this time, we need to use the work-energy theorem. The work (W) done by the torque can be calculated using the equation:
W = (1/2) * I * ω^2,
where I is the moment of inertia and ω is the initial angular velocity.
Given the values of I and ω, we can substitute them into the formula to find W.
Now, armed with these explanations and the formulas, you can proceed to calculate the answers to each part of the problem.