Question

A cruise ship with a mass of 1.00×10⁷ kg strikes a pier at a speed of 0.750 m/s. Calculate the average force exerted on the pier using the concept of impulse. (Hint: First calculate the time it took to bring the ship to rest, assuming a constant force.)

a) 6.0 x 10^5 N
b) 7.5 x 10^5 N
c) 8.0 x 10^5 N
d) 9.0 x 10^5 N

Answer 1

To calculate the average force exerted on the pier, we can use the concept of impulse. The equation for impulse is I = F * Δt. We need to find the time it took to bring the ship to rest using the equation for average velocity.

Step-by-step explanation:

To calculate the average force exerted on the pier, we can use the concept of impulse. Impulse is defined as the change in momentum of an object, and it is equal to the force acting on the object multiplied by the time the force is applied. In this case, the cruise ship comes to rest after traveling 6.00 m, so the change in momentum is equal to the initial momentum. We can calculate the initial momentum using the mass and initial velocity of the ship. The impulse is also equal to the average force multiplied by the time it takes to bring the ship to rest. We can rearrange this equation to solve for the average force.

The equation for impulse is:

I = F * Δt

Given:

m = 1.00 * 10^7 kg
V₁ = 0.750 m/s
Δx = 6.00 m

First, we need to find the time it took to bring the ship to rest. We can use the equation for average velocity to calculate the time:

V_avg = Δx / Δt