A 2.00-kg stone is sliding to the right on a frictionless...

A $2.00-\mathrm{kg}$ stone is sliding to the right on a frictionless horizontal surface at 5.00 $\mathrm{m} / \mathrm{s}$ when it is suddenly struck by an object that exerts a large horizontal force on it for a short period of time. The graph in Fig. 8.34 shows the magnitude of this force as a function of time. (a) What impulse does this force exert on the stone? (b) Just after the force stops acting, find the magnitude and direction of the stone's velocity if the force acts (i) to the right or (ii) to the left.

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Key Concepts

Vector Analysis in Dynamics

Considering that both force and momentum are vector quantities, vector analysis is crucial in dynamics. This involves accounting for magnitudes and directions, ensuring that proper sign conventions are applied when evaluating the impact of forces acting in different directions.

Momentum

Momentum is the product of an object's mass and velocity. As a vector quantity, it describes both the magnitude of motion and its direction, and it plays a central role in analyzing dynamics and collisions.

Impulse

Impulse is the physical quantity defined as the integral of force over the time interval during which it acts. It represents the cumulative effect of a force applied over a specific period and is directly related to the change in momentum of an object.

Impulse-Momentum Theorem

The impulse-momentum theorem links the impulse applied to an object to its change in momentum. By equating the impulse to the difference between the final and initial momentum, this theorem provides a fundamental method for calculating the effects of forces over time.

Transcript

00:01 Problem.

00:01 8 13 we have a stone sliding along a frictionless surface.

00:08 It's going five meters per second at the beginning of time as a massive two kilograms.

00:15 And then this stone is moving along, minding its own business, and then some rather large force wax it for a millisecond.

00:23 Um, so we need to figure out what what the aftermath of that is going to look like.

00:30 So the first thing to note is the units of the scale of this.

00:34 Does this contribute up easily if you don't pay close attention, like you should with any grab the time here is in milliseconds.

00:41 So this is only acting over a millisecond.

00:44 And this isn't killing a newton's.

00:47 So this is actually 2500 newtons.

00:51 Obviously, we need the right numbers to get the right numbers out of you know what we do here.

00:58 So the first part that we need to do, he's just to find the impulse.

01:02 And this has nothing to do with the stone because, as we know, the impulse for a constant force is just equal to the value of that forest times the amount of time it's being.

01:19 So we have 2500 newtons.

01:30 No one notices, and unsurprisingly, this comes out two and 1/2 newton seconds also kilogram, meters per second, the same units of momentum which will become important soon...

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