Two types of energy-absorbing fenders designed to be used on...

Two types of energy-absorbing fenders designed to be used on a pier are statically loaded. The force-deflection curve for each type of fender is given in the graph. Determine the maximum deflection of each fender when a 90 -ton ship moving at $1 \mathrm{mi} / \mathrm{h}$ strikes the fender and is brought to rest.

Key Concepts

Energy Absorption in Impact Scenarios

Energy absorption involves the transformation of kinetic energy into other forms of energy, such as elastic potential energy, through deformation of a material. This concept is central in designing systems like fenders intended to mitigate impacts, ensuring that they can safely dissipate the energy from collisions.

Force-Deflection Curve

A force-deflection curve shows how the force exerted by a material or system varies with the amount of deformation. The area under the curve represents the work done and thus the energy absorbed by the material. In evaluating fender performance, this area is crucial for determining how much deflection will occur when absorbing a given amount of kinetic energy.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion, calculated by the formula ½ * mass * velocity². In the context of an impact, this energy must be absorbed to bring the object to a stop, and it represents the total energy that the fender must dissipate during the collision.

Work-Energy Principle

The work-energy principle states that the work done by forces acting on an object is equal to the change in its kinetic energy. For the ship coming to rest, the work done by the fender—found by integrating the force over the amount of deflection—must equal the ship’s kinetic energy.

Transcript

00:01 Hey everyone, thanks for joining us today.

00:02 What we're going to be looking at again is the concept of work and kinetic energy.

00:07 And what we have is we have two fenders with their loading curves shown here in the graph in a and b.

00:15 So a is linear.

00:16 B is some sort of exponential.

00:18 We're given the mass of a ship that is 90 tons and it is moving at a velocity of one mile an hour.

00:25 And what we're asked to solve for is what is the deflection of these bumpers when that's, ship is brought to rest.

00:32 So first thing we're going to do is we're going to figure out the slopes of the linear bumper.

00:40 And what you find is that the slope of the linear bumper is going to be 60 ,000 and then 60 ,000 pound per feet times x, which is going to be the expression that we use to describe the force with respect to the distance.

01:07 And then what we're going to do is we're going to convert the mass of the ship into pounds so we know that the mass of the ship is 90 tons.

01:15 You know, it's the weight of the ship actually and that we're going to convert that to 18 ,000 pounds.

01:24 We know the velocity of the ship is one mile an hour and we're going to convert that to feet per second and that is 1 .47 feet per second.

01:37 Now we know that the relationship between work and kinetic energies as follows, we know that the initial kinetic energy plus the work that's done is equal to the final kinetic energy.

01:49 So we know that the initial kinetic energy is simply 1 half mv squared, and that the boat is brought to rest.

01:58 So the final kinetic energy is zero...

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