Question

We return to the same well where we dropped our phone at the start of this class and now are curious about the bucket lowering mechanism sitting at the top. The bucket (m = 2 kg) is attached to a string that is wrapped around a cylinder (M = 1 kg, R = 2 cm) that rotates through an axle around its center. The bucket is released from a height of 1 meter above the surface of the water. How long does it take for the bucket to reach the water

Answer 1

The bucket will reach the water in approximately 0.45 seconds when dropped from a height of 1 meter, assuming no air resistance and a frictionless pulley system.

Step-by-step explanation:

To calculate the time it takes for a bucket to reach the water when dropped from a height of 1 meter, we apply the equations of motion under uniform acceleration (gravity). Since air resistance and friction in the pulley system are ignored, the bucket's acceleration will be equal to the acceleration due to gravity, which is approximately 9.81 m/s2. Assuming the bucket starts from rest, we can use the following second equation of motion:

s = ut + (1/2)at2

Here, s is the displacement (1 meter), u is the initial velocity (0 m/s, since the bucket starts from rest), a is the acceleration due to gravity (9.81 m/s2), and t is the time we need to find. Plugging in the values, we get:

1 = 0 * t + (1/2)(9.81)t2

t2 = 2/9.81

= 0.2039

t = √0.2039

≈ 0.45 seconds

So, it takes approximately 0.45 seconds for the bucket to reach the water's surface.