Question

Be sure to review Example 10.3 before attempting these VP 10.3.1 problems. Part A A bucket with mass m=1.0 kg is suspended over a well by a winch and rope (Eigure 1). The winch consists of a solid cylinder with mass 4.0 kg and radius R=0.10 m about which the rope is wrapped. A handle is attached to one end in order to rotate the cylinder. For the purposes of this example, we are going to ignore any frictional forces in the winch. Now suppose that the winch hancle breaks off, allowing the bucket to fall to the water as the rope unwinds from the cylinder. Assume that the bucket is released at t=0 and the water level is at a depth h=2.7 m below the bucket at t=0. How far above the water is it at 0.50 s ? Figure Express your answer with the appropriate units. * Incorrect; Try Again; 3 attempts remaining

Answer 1

The bucket is 0.615 m above the water at 0.50 s.

Step-by-step explanation:

To determine how far above the water the bucket is at 0.50 s, we can use the equations of motion. We need to find the displacement of the bucket along the vertical direction.

Using the equation h = ut + (1/2)gt^2, where h is the displacement, u is the initial velocity, g is the acceleration due to gravity, and t is the time, we can calculate the displacement.

Since the bucket is released from rest, its initial velocity is 0. The acceleration due to gravity is -9.8 m/s^2 in the upward direction. Plugging in the values, we get h = (1/2)(-9.8)(0.50)^2 = -0.615 m.

Answer 2

To find the bucket's position after 0.5 seconds of free fall, the distance fallen is calculated using the kinematic equation for motion with constant acceleration. The result is subtracted from its initial height above the water, yielding a remaining height above the water of approximately 1.47 m.

Step-by-step explanation:

The problem given is a physics problem involving kinematics and the motion of an object under the influence of gravity. We are tasked to calculate the position of a bucket after 0.5 seconds as it falls down a well, with no initial velocity and no friction from the winch.

Given that the bucket starts from rest, we can use the equation of motion under constant acceleration due to gravity (g = 9.81 m/s2):

d = ½ g t2

Where:

• d is the distance fallen
• g is the acceleration due to gravity
• t is the time elapsed

Substituting the given values:

d = ½ × 9.81 m/s2 × (0.5 s)2

d = 1.22525 m (approximately 1.23 m)

The bucket was initially 2.7 m above the water, so to find how far it is above the water after 0.5 s, we subtract the distance fallen from the initial height:

Remaining distance above water = Initial height - Distance fallen

Remaining distance above water = 2.7 m - 1.22525 m

Remaining distance above water = 1.47475 m

The bucket is approximately 1.47 m above the water after 0.5 seconds.