A 20 kg crate is subject to a force having a constant...

A 20 kg crate is subject to a force having a constant direction and magnitude of F = 100 N at 30 degree from the horizontal. The crate is moving to the right with an initial speed of 8 m/s. The coefficient of kinetic friction between the crate and the ground is μk = 0.25. a) Draw the free body diagram of the crate. [2 marks] b) Using Newton’s Laws of motion, determine the speed of the crate when it is moved a distance, s = 21 m, [4 marks] c) Using energy conservation law, recalculate its speed when s=21 m. [4 marks]

Transcript

00:01 So in this problem, we have a crate given as m equal to 20 kilograms for the mass being pulled at an angle 30 degrees.

00:10 And the force of that pull is given as 100 newtons, and the angle again, theta equals 30 degrees.

00:18 And we're told that when this crate that's being pulled, in the distance, s1 is 15 meters, the speed of this crate, v1, is 8, meters per second.

00:36 So we're asked to find the speed v2 and the distance we'll call s2 is 25 meters.

00:49 So now because we're dealing with forces we want to make a free body diagram right away just so we can see what forces we're dealing with in the x and the y direction.

01:04 Free body diagram you know that there's a force going down which is the weight that's given as mg and so there's an opposite force, normal force, fn, and we have a force on the right side at some angle 30 degrees, which means that we can break this up into components to make your calculations easier.

01:29 We have force in the x direction f of x, force in the y direction f of y and by simple geometry we know that f of y is f sine theta f of x, f, cosine data.

01:51 And we're also told that when this crate is being pulled, there's friction in the opposite direction.

01:58 We'll call it fk, this is friction due to kinetic motion.

02:03 And we're also given the coefficient of kinetic friction in uk.

02:10 0 .25.

02:13 Okay, so now we find the forces in each direction.

02:21 So let's start with.

02:23 F of x.

02:25 So in the x direction, we have just f of x and the force due to the kinetic friction...