Question

You are unloading a refrigerator from a delivery van. The ramp on the van is 5.0 mm long, and its top end is 1.4 mm above the ground. As the refrigerator moves down the ramp, you are on the down side of the ramp trying to slow the motion by pushing horizontally against the refrigerator with a force of 270 NN .How much work do you do on the refrigerator during its trip down the ramp?W = ???

Answer 1

Answer:

Work done is 1.31 J.

Explanation:

Given:

Length of the ramp (L) = 5.0 mm

Height of the top end (H) = 1.4 mm

Horizontal force applied (F) = 270 N

Work done (W) = ?

We know that,

Work done is equal to the product of force and displacement caused along the line of application of force.

Here, the force acting on the refrigerator is in the horizontal direction while the refrigerator is moving down along the length of the ramp. So, we have to first find the horizontal component of the displacement caused.

Now, consider the triangle ABC representing the given situation. The point A is the top end point of the ramp, AB is the length of the ramp, AC is the vertical displacement of the refrigerator and BC is the horizontal displacement of the refrigerator.

Using Pythagoras theorem,

$AB^2=BC^2+AC^2\\\\(5.0)^2=BC^2+(1.4)^2\\\\BC=\sqrt{25.0-1.96}\\\\BC=4.86\ mm$

Now, force applied on the refrigerator is in the direction opposite to the horizontal component of displacement. So, work is negative.

Work = Force × Horizontal displacement

$W=270\ N\times 4.86\ mm\\\\W=1312.2\ \textrm{N-mm}\\\\W=1.31\ J\ \ \ \ \ \textrm{ [1 mm = 0.001 m]}$

Therefore, work done is 1.31 J.