Suppose a box on a frictionless ramp is being pulled by a rope with a tension of 350 N making an angle of 50 degrees to the horizontal ground.If the angle of incline of the ramp is 20 degrees, and...

Suppose a box on a frictionless ramp is being pulled by a rope with a tension of 350 N making an angle of 50 degrees to the horizontal ground.

If the angle of incline of the ramp is 20 degrees, and the box is pulled 5 m, determine the amount of work done.

Asked on by rosemin

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The tension in the rope used by which the box is being moved is equal to 350 N. The rope makes an angle of 50 degrees with the horizontal.

The box is on a ramp inclined at 20 degrees. It is pulled a distance equal to 5 m using the rope.

We can divide the force exerted by the rope on the box into two components, one that is in the direction of motion of the box and another which is perpendicular to the direction of motion of the box.

Work is done only by the component that is in the direction of motion of the box. This is equal to: 350* cos (50 - 20)

=> 350* cos 30

=> 350* (sqrt 3 / 2)

=> 175* sqrt 3

The work done is force* distance = 175* sqrt 3 * 5

=> 875* sqrt 3

=> 1515.5 J

The work done in pulling the box is equal to 1515.5 J

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