A person is making homemade ice cream. She exerts a force of magnitude 17 N on the free end of the crank handle, and this end moves in a circular path of radius 0.28 m. The force is always applied parallel to the motion of the handle. If the handle is turned once every 2.0 s, what is the average power being expended?
The work done every 2 seconds is
W = 2 pi R * F = 6.28*0.28*17 Joules
Divide that by 2 seconds for the power in Watts.
P = W/t = 6.28*0.28*17/2 = 15.3 Watts
To find the average power being expended, we need to calculate the work done every 2 seconds and then divide it by 2 seconds.
First, let's calculate the work done every 2 seconds:
W = 2πRF
Where:
W is the work done
π is approximately 3.14
R is the radius of the circular path (0.28 m)
F is the magnitude of the force applied (17 N)
W = 2 * 3.14 * 0.28 * 17
W ≈ 30.2464 Joules (rounded to four decimal places)
Now, to find the average power being expended, we divide the work done by the time it takes (2 seconds):
P = W / t
Where:
P is the average power
W is the work done (30.2464 Joules)
t is the time (2 seconds)
P = 30.2464 / 2
P ≈ 15.1232 Watts (rounded to four decimal places)
Therefore, the average power being expended is approximately 15.1232 Watts.
To find the average power being expended, we can start by calculating the work done every 2 seconds.
The formula for work is given by
W = F * d * cos(theta)
In this case, the force (F) is 17 N, the distance traveled (d) is given by the circumference of the circular path traveled by the handle, which is 2 * pi * radius (0.28 m), and the angle (theta) between the force and the displacement is 0° since the force is parallel to the motion of the handle.
Substituting the values into the equation, we have:
W = 17 N * (2 * pi * 0.28 m) * cos(0°)
W = 17 N * (2 * pi * 0.28 m)
Calculating this yields:
W ≈ 30.21 J (Joules)
Next, we divide the work by the time taken to perform it, which is 2 seconds, in order to find the average power:
Average Power = W / t
Average Power = 30.21 J / 2 s
Calculating this gives us:
Average Power ≈ 15.10 W (Watts)
Therefore, the average power being expended is approximately 15.10 Watts.