Question

The motion of a ship with weight 48000 -lb is slowed using bumpers on a dock which exerts a force on the ship according to relationship F=4000s3. The initial velocity of the ship is v=2.6ft/s. What is the change in kinetic energy of the ship? T2​−T1​=

Answer 1

To calculate the change in kinetic energy of the ship, we need to find the mass of the ship and the final velocity using the force exerted by the bumpers. Once we have those values, we can plug them into the equation for change in kinetic energy.

Step-by-step explanation:

Given:

Weight of the ship (W) = 48000 lb

Force exerted by the bumpers (F) = 4000s^3

Initial velocity of the ship (v) = 2.6 ft/s

The change in kinetic energy of the ship (T2 - T1) can be calculated using the equation:

T2 - T1 = 0.5 * m * v2^2 - 0.5 * m * v1^2

Where m is the mass of the ship and v1 and v2 are the initial and final velocities, respectively.

First, we need to find the mass of the ship using the weight:

Mass (m) = Weight (W) / acceleration due to gravity (g)

Assuming the acceleration due to gravity is 32.2 ft/s^2,

m = 48000 lb / 32.2 ft/s^2

Next, we need to find the final velocity (v2) using the force exerted by the bumpers:

F = ma

4000s^3 = m * a

Since a = (v2 - v1) / t (where t is the time taken for the ship to stop),

4000s^3 = m * (v2 - 2.6 ft/s) / t

Lastly, plug the values into the equation for change in kinetic energy:

T2 - T1 = 0.5 * m * v2^2 - 0.5 * m * (2.6 ft/s)^2