A box is given a push across a horizontal surface. The box...

A box is given a push across a horizontal surface. The box has a mass $m$, the push gives it an initial speed of 1.90 m/s, and the coefficient of kinetic friction between the box and the surface is 0.105. (a) Use energy considerations to find the distance (in m) the box moves before it stops. m (b) What If? Determine the stopping distance (in m) for the box if its initial speed is doubled to 3.80 m/s. m

Transcript

00:01 In this problem, we have a box, and i'm going to draw a free body diagram.

00:04 And it's on a horizontal surface.

00:06 So that means the force and the gravity, it's going down, normal force is going directly up.

00:13 It's given a push, and it moves on initial speed.

00:16 And so since it's on a flat surface, we know the sum of the forces and the y direction will equal to zero.

00:25 It is given an initial velocity from this push of 1 .9 meters per second, we're now.

00:32 Not given the mass of the object.

00:34 We're just told it equals to mass.

00:36 We're given a coefficient of friction so that tells us there is friction present.

00:40 So we'll add that to our diagram.

00:43 And that is 0 .150.

00:47 And we want to know using energy equations, how far does this box move before it comes to a stop? so that means final velocity is zero.

00:58 And we're looking for distance.

01:01 Right.

01:01 So the only force being applied to it is friction be into a stop.

01:05 Even though it was given a push, it's not being constantly pushed.

01:08 And so we're looking at the point after the push has happened and given that box the speed of 1 .9.

01:14 So what equation would be our energy equations? well, we know work is equal to change in energy.

01:20 And the energy that's changing here deals with speed.

01:23 So this will be our change in kinetic energy.

01:26 That means k -e -final minus k -e initial.

01:31 And so if we were to expand this to include distance, which is what we're looking for, would be force times distance is equal to one -half mass velocity final squared, which we know that final velocity is zero.

01:44 So this whole thing is zero, minus one -half mass velocity initial squared.

01:50 So what force is causing this change in energy? it is the frictional force.

01:56 So this is the force of friction.

01:58 Well, we're not given the force of friction, but we are given the coefficient of friction.

02:03 So we can come over here and write that equation.

02:05 The coefficient of friction is equal to force of friction divided by normal force.

02:11 Well, we have coefficient of friction, but we don't have normal force...

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