Question

A washing machine drum 72.0 cm in diameter starts from rest and achieves 1200.0 rev/min in 20.0 s. Assume the acceleration of the drum is constant.

1) Calculate the magnitude of the net acceleration of a point on the drum after 1.00 s has elapsed. (Express your answer to three significant figures.)

2) Specify the direction of the net acceleration of a point on the drum after 1.00 s has elapsed. (Express your answer to two significant figures.)

Answer 1

Answer 2

To solve this problem, we'll first calculate the angular velocity of the drum after 1 second, and then we'll find the magnitude and direction of the net acceleration of a point on the drum at that time.

Given data: Diameter of the drum (d) = 72.0 cm Radius of the drum (r) = 72.0 cm / 2 = 36.0 cm = 0.36 m Time (t) = 1.00 s

1. Calculate the magnitude of the net acceleration after 1.00 s has elapsed:

Angular velocity (ω) can be calculated using the formula:

ω = (final angular velocity - initial angular velocity) / time

We are given that the drum achieves 1200.0 rev/min (revolutions per minute) after 20.0 s. We need to convert this angular velocity to radians per second to be consistent with SI units.

Angular velocity in radians per second (ω) = (1200.0 rev/min) * (2π rad/rev) / (60 s/min) ≈ 125.66 rad/s

Now, we can calculate the angular acceleration (α) using the formula:

α = ω / t

α = 125.66 rad/s / 20.0 s ≈ 6.283 rad/s²

Next, we can find the linear acceleration (a) of a point on the drum using the formula:

a = r * α

a = 0.36 m * 6.283 rad/s² ≈ 2.26 m/s²

So, the magnitude of the net acceleration of a point on the drum after 1.00 s has elapsed is approximately 2.26 m/s².

2. Specify the direction of the net acceleration after 1.00 s has elapsed:

The direction of the net acceleration is tangential to the circular path of a point on the drum. In this case, the acceleration is directed in the same direction as the velocity of the point on the drum, which is along the tangent to the circular path at that point.

Therefore, the direction of the net acceleration of a point on the drum after 1.00 s has elapsed is tangential to the circular path and points in the direction of motion.