Question

A box is at rest on a ramp at an incline of 22°. The normal force on the box is 538 N.

Answer 1

Answer: 580 N

Refer to attached figure.

The angle of inclination is 22 degrees

weight (gravitational force) acts downwards.

Normal force is a contact force which acts perpendicular to the point of contact.

The horizontal component (mg cos 22 ) balances the normal force and the vertical component balances the frictional force.

Gravitational force on an object = mg

The normal force $N= mg cos 22$

$\Rightarrow mg =\frac{N}{cos22}=\frac{538 N}{0.927}=580 N$

Answer 2

Answer

580

Explanation

The gravitational force acts perpendicularly downwards (towards the center of the earth).

The normal force of the box  is perpendicular to the slanting ramp. This force we are given 538 N.

The gravitational force is the component of this 538 N.

∴ Cos22° = 538/Y  Where y is the gravitational force.

  Cos22° = 538/Y

  Y× Cos22° = 538

  Y = 538/Cos22°

    = 580.25

Answer to the nearest whole number = 580.