A block of mass 16.2 kg is sliding at an initial velocity of...

A block of mass 16.2 kg is sliding at an initial velocity of 7.65 m/s in the positive x-direction. The surface has a coefficient of kinetic friction of 0.173. (Indicate the direction with the signs of your answers.) HINT (a) What is the force of kinetic friction (in N) acting on the block? N (b) What is the block's acceleration (in $m/s^2$)? m/s$^2$ (c) How far will it slide (in m) before coming to rest? m

Transcript

00:01 Hi there, so for this problem we have a log with the mass that is given, and the mass for that is equal to 18 .2 kilograms, and it is sliding at an initial velocity that is given, and that initial velocity is 5 .15 meters per second.

00:22 This in the positive x direction.

00:25 Now the surface has a coefficient of friction that is given and that coefficient of friction is 0 .173.

00:39 Okay, now once we have this, the question is for part a of this problem, is what is the force of kinetic friction? okay, now let me first draw all of the forces acting on this object, on these bumps.

00:56 So we have the normal force that is always perpendicular to the surface.

01:01 And we have the frictional force that opposes the motion of this.

01:10 And of course we have the weight of this, which is just the mass times acceleration due to gravity.

01:16 Then we apply newton's second law to the forces acting on the x direction.

01:25 We only have the frictional force that is equal to the mass times the acceleration.

01:33 Now we know that the frictional force is defined as the normal force times the coefficient of kinetic friction.

01:40 Now, from newton's second law to the forces applied in the y direction, we will have that the normal force minus the weight is equal to zero.

01:48 Then solving for the normal force, that will be equal to the weight.

01:52 So that is what we need to substitute in here.

01:55 Then the frictional force is equal to the normal force, which is equal to the weight times the coefficient of kinetic friction.

02:02 And now we substitute the values in here, so that will be done.

02:06 The mass for this, that is 18 .2.

02:09 This times acceleration due to gravity, that is 9 .8 times the coefficient of kinetic friction, which is 0 .173.

02:21 Okay, then using our calculator, we obtain a value of 30 .86.

02:39 This with two decimal places.

02:43 Okay, 30 .86 newtons.

02:55 So that's a solution for part a of this problem.

02:59 Now for part b, we are asked about what is the bloch's acceleration? now remember that the frictional force, which is the only force acting on that direction is equal to the mass times acceleration.

03:14 So the acceleration is that the frictional force that we obtained from before divided by the mass of this...

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