A person is making homemade ice cream. She exerts a force of magnitude 23 N on the free end of the crank handle, and this end moves in a circular path of radius 0.35 m. The force is always applied parallel to the motion of the handle. If the handle is turned once every 1.6 s, what is the average power being expended?

Force * distance/time = Power

In this case the distance is 2 pi R

To find the average power being expended, we need to use the formula:

Average Power = Work / Time

The work done is given by:

Work = Force * Distance

In this case, the force applied is parallel to the motion of the handle, so the work done can be calculated using the formula for circular motion:

Work = Force * Distance * Cos(θ)

where θ is the angle between the force and the direction of motion. Since the force and motion are parallel, θ = 0, thus Cos(θ) = 1.

The distance traveled in one revolution is equal to the circumference of the circular path, which is given by:

Distance = 2π * radius

Let's calculate the work and then use it to find the average power.

Given:
Force (F) = 23 N
Radius (r) = 0.35 m
Time (t) = 1.6 s

First, let's calculate the distance:

Distance = 2π * radius
= 2 * 3.1416 * 0.35
≈ 2.19911 m

Next, let's calculate the work:

Work = Force * Distance
= 23 * 2.19911
≈ 50.58053 J

Now, let's calculate the average power:

Average Power = Work / Time
= 50.58053 / 1.6
≈ 31.61283 W

Therefore, the average power being expended is approximately 31.61283 Watts.

To find the average power being expended, we need to first calculate the work done and then divide it by the time taken.

The work done can be calculated using the formula:

Work = force × distance × cos(theta)

In this case, since the force is always applied parallel to the motion of the handle, the angle theta between the force and displacement is 0 degrees, so cos(theta) = 1.

Distance = circumference of circular path = 2πr, where r is the radius of the circular path.

So, the work done can be calculated as:

Work = force × distance = 23 N × 2π(0.35 m)

Next, we need to calculate the time taken for one complete revolution of the handle, which is given as 1.6 s.

Finally, the average power expended can be calculated as:

Average Power = Work / Time

Now, let's substitute the values and calculate:

Distance = 2π(0.35) = 2.2π m (approximately)

Work = 23 N × 2.2π m ≈ 50.97 Nm

Average Power = 50.97 Nm / 1.6 s ≈ 31.86 Watts (approximately)

Therefore, the average power being expended is approximately 31.86 Watts.

Well, making homemade ice cream is quite a cool endeavor! Let's crunch some numbers for your power query.

Power (P) is equal to the work done (W) divided by the time it takes (t):
P = W / t

Now, work (W) is defined as the force (F) applied multiplied by the distance (d) traveled in the direction of the applied force:
W = F * d

In this case, the force applied is given as 23 N. The distance traveled is the circumference of the circular path, since the handle is turning in a circle. The circumference is found using the formula:
C = 2 * π * r

Given that the radius (r) is 0.35 m, we can calculate the circumference (C). But since the force is always parallel to the motion, the distance traveled is only half the circumference (since only half a turn is made per second). Therefore, the distance (d) is:
d = C / 2 = (2 * π * r) / 2

With these values, we can now calculate the work:
W = F * d = 23 N * [(2 * π * 0.35 m) / 2]

Now for the final touch! Since the handle is turned once every 1.6 s, we can substitute these values into the power equation:
P = W / t = [23 N * (2 * π * 0.35 m) / 2] / 1.6 s

Calculate that, and you have the average power being expended! But remember, power is no piece of cake!

.35 * 2 = .7

23 * .7 = 16.1J
P = 16.1/1.6 = 10.06W