In a crash test, a 1240-kg car slams into a concrete wall at 17.9 m / s and comes to rest in 0.

In a crash test, a 1240-kg car slams into a concrete wall at...

In a crash test, a $1240-\mathrm{kg}$ car slams into a concrete wall at $17.9 \mathrm{~m} / \mathrm{s}$ and comes to rest in $0.275 \mathrm{~s}$. (a) Find the magnitude of the impulse delivered to the car. (b) Find the average stopping force.

Key Concepts

Average Force

Average force refers to a constant force that, when applied over a specified time interval, would result in the same total impulse as the actual, possibly variable, force. It is calculated by dividing the total impulse by the time during which the force was applied, providing a simplified measure for analyzing the effects of forces in impact situations.

Impulse-Momentum Theorem

The impulse-momentum theorem states that the impulse on an object equals the change in its momentum. This principle allows one to determine how forces acting over a specific time interval alter the velocity and momentum of an object, making it especially useful in crash and collision scenarios.

Impulse

Impulse is a measure of the effect of a force acting over a time interval, defined as the product of the force and the time during which it is applied. It represents how much the momentum of an object changes when a force is applied, and it is calculated by integrating the force over the time period of its application.

Momentum

Momentum is the product of an object’s mass and its velocity, representing the quantity of motion the object possesses. In dynamics, momentum is a key concept because changes in an object’s momentum are directly related to the impulses it experiences, making it fundamental for analyzing collisions and impacts.

Transcript

00:02 This lesson, we're going to talk about the relationship between force, impulse, and momentum.

00:08 So we're going to do this looking at the example of a car.

00:11 I can't really draw crashing into a wall.

00:21 And the problem gives us the car's initial velocity, which is 17 .9 meters per second.

00:32 And we have the car's mass, which is 1 ,240 kilograms.

00:41 And we also have the time it takes the car to stop once it hits the wall.

00:45 And that is given as a little over a quarter of a second, which is two, seven, five seconds.

00:56 What we want to do is find the impulse that the car feels from the wall, and we want to find the average force that the wall imparts on the car stopping it.

01:08 Right.

01:08 So how do we do this? so we have a couple of equations that are going to be helpful in some.

01:13 This first is the equation for momentum, which is momentum equals mass, which we have times velocity, which we also have.

01:24 And we also have a relationship between momentum and force or impulse and force.

01:32 So we know the impulse is going to equal the change in momentum, which is also going to equal force times, times.

01:47 That the force is acting, which we also have from the problem.

01:51 All right.

01:53 So impulse.

01:54 Let's look at that one first.

01:57 Impulse.

01:59 I think your book uses j, so i'll just use that for now, equals the total change in momentum...

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