Rotation Dynamics mastering physics 10.32

[wku_tops]

An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airplane's engine is first started, it applies a constant torque of 1950 Nm to the propeller, which starts from rest.

How much work in joules is being done after 5 revolutions?

This is what I did: (1.04*1950)*(5*2*pi). Mastering physics says it is close, but not correct.

 

[wku_tops]

figured that out: (1950)*(5*2pi)
Now I need to calculate the average power. power=T_z*w_z
=1950 Nm *53.9 rads/s.

mastering physics says this is incorrect. Any ideas?

 

[quicknote]

Your calculation appears to be on the right track, but there may be some minor errors in the units used. Let's break down the problem step by step to make sure we are getting the correct answer.

First, let's convert the length of the propeller from meters to centimeters, since the torque is given in Newton-meters. This gives us a length of 208 cm.

Next, we need to find the moment of inertia of the propeller. This can be calculated using the formula I = (1/12)*m*L^2, where m is the mass and L is the length of the propeller. Plugging in the values, we get I = (1/12)*(117 kg)*(208 cm)^2 = 26000 kg*cm^2.

Now, we can use the formula for rotational work, W = (1/2)*I*ω^2, where ω is the angular velocity. Since we are interested in the work after 5 revolutions, we can find the angular velocity using the formula ω = 2π*n/t, where n is the number of revolutions and t is the time it takes to complete those revolutions. In this case, n = 5 and t = 5 revolutions/revolutions per second = 1 second. Therefore, ω = 2π*5/1 = 10π rad/s.

Plugging this value into the work formula, we get W = (1/2)*(26000 kg*cm^2)*(10π rad/s)^2 = 1300000 kg*cm^2/s^2 = 1300000 J.

So, the work being done after 5 revolutions is 1300000 J, or 1.3 MJ.

It's possible that the slight discrepancy between your answer and the one given by Mastering Physics is due to rounding errors or differences in unit conversions. Make sure to check your calculations and use consistent units throughout.