A small box with mass 0.600 kg is placed against a...

A small box with mass 0.600 kg is placed against a compressed spring at the bottom of an incline that slopes upward at 37.0° above the horizontal. The other end of the spring is attached to a wall. The coefficient of kinetic friction between the box and the surface of the incline is ?k = 0.400. The spring is released and the box travels up the incline, leaving the spring behind. Part A What minimum elastic potential energy must be stored initially in the spring if the box is to travel 2.00 m from its initial position to the top of the incline?

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Transcript

0:00 Hello.

00:01 Here we have to calculate the minimum potential energy which must be stored by spring to push the box two meters from its initial position to the top of the incline.

00:16 So let's show the system that is the incline with an angle alpha.

00:24 And the box is connected to the spring which is compressed and it has some initial potential energy of the p .e .0.

00:40 Then the box is pushed by the spring and it travels to its final position.

00:46 So in the way that the overall displacement is l.

00:52 And here the mass of the box is 0 .600 kilograms.

00:59 Angle alpha is 37 degree and coefficient of kinetic friction is 0 .400.

01:07 The distance traveled by the box is 2 .00 meters and we have to find minimum potential energy which is needed.

01:23 Let's do this.

01:25 So the requirement for the minimum potential energy indicates that here where the box stops it has only potential energy.

01:37 So it means that this initial potential energy equals to the size.

01:42 Sum of the final potential energy plus absolute work of the friction force.

01:52 So to find the work done by the friction force, we have to look at the forces which exerts in this system.

02:02 The first one is reaction of the surface, then gravity, and also the friction force.

02:11 Let's introduce x and y axis...

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