The crate, which has a mass of 100 kg, is subjected to the action of the two forces. If it is or

The crate, which has a mass of 100 kg, is subjected to the...

Key Concepts

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This principle is essential for analyzing the motion of an object when multiple forces, such as an applied force and friction, are involved.

Kinetic Friction

Kinetic friction is the resistive force that opposes the relative motion of two surfaces in contact when they slide against each other. It is calculated by multiplying the coefficient of kinetic friction by the normal force, and it plays a crucial role in determining the net force acting on an object in motion.

Work-Energy Principle

The work-energy principle states that the work done by all forces acting on an object is equal to the change in its kinetic energy. This concept is particularly useful for problems where forces such as friction and applied forces do work along the displacement, leading to changes in speed.

Kinematic Equations

Kinematic equations relate the parameters of motion—displacement, initial velocity, final velocity, acceleration, and time—in situations of constant acceleration. These equations allow for calculating one of these variables when the others are known, making them valuable for analyzing motion resulting from a net force.

Transcript

00:01 On this problem, we have a crate that's being pulled on the right side of the force of 1 ,000 newtons.

00:07 On the left side, it's being pushed with a force of 800 newtons at an angle of 30 degrees.

00:13 And you want to find the distance s that this crate travels when the velocity is 6 meters per second, which we'll call v2.

00:25 And we're also given coefficient of kinetic friction .2 and the mass of this crate than 100 kilograms so because we're dealing with forces we want to calculate the distance traveled we can use the equation for work which is just force times distance but we also are given a velocity because of that we know that there's a kinetic energy involved because kinetic energy deals with movement so that means we can combine those two and use the work energy principle, which is given as the initial kinetic energy of the object, plus the work being done on the object is equal to its final kinetic energy.

01:11 Because the object is initially at rest, initial kinetic energy is zero because the velocity is zero.

01:20 So now we're just left with the work being done on the object is equal to its final kinetic energy.

01:29 We can expand this a little bit.

01:30 So the work being done is the force and this force is in the x direction because that's the where the movement is that times the distance travel is equal to 1 half m d2 squared.

01:48 We'll call this equation 1.

01:52 So in order to solve s we need to find the force in the next direction.

01:58 So to do that, we use a free body diagram.

02:04 So that we can see all the forces on this crate and then find what what they are in the x direction.

02:14 So we have the weight pushing down on the crate which is just mass times gravity.

02:21 Then we have a force in the opposite direction, a normal force fn.

02:29 And on the right side we have that force with 1 ,000 newtons and we're given a triangle here to make the calculations a little easier.

02:40 This helps with the components.

02:44 So we have this triangle of a hypotenuse of 5, bottom part 4, and the right side 3.

02:51 So that means on the right side, the x direction is 1 ,000 times the x component.

03:01 And looking at this triangle, you want to find the bottom part.

03:04 So that means the x component is a ratio of 3 fifth.

03:07 So it's 1 ,000 times 3 fits.

03:12 In the y direction was just the right side.

03:18 So it'll be 1 ,000 times four -fits.

03:27 Now on the left side, we have that force that's pushing the crate of 800 newtons.

03:35 And then this has components...

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