Question

A man of mass M is on a weighing machine placed on a wedge of inclination theta with horizontal. If weighing machine, man and wedge are assumed to be at rest, weight of man registered by the weighing machine is
1. M
2. M sin theta
3. M cos theta
4. M tan theta

Answer 1

Given:

A man of mass M is on a weighing machine placed on a wedge of inclination theta with horizontal.

To find:

Weight of man as registered by the weighing machine.

Assumptions:

Weighing machine , man and wedge are at rest.

Calculation:

Weighing machine indicates the force (thrust) provided normal (at 90°) to the surface on which the machine has been kept.

So, weight of the man on the wedge can be resolved into two perpendicular components:

• Along the inclined plane

• Perpendicular to inclined plane

So, weighing machine wheel show the component which is perpendicular to the inclined plane

$\boxed{ \sf{W = Mg \cos( \theta) }}$

Refer to the attached diagram.

Answer 2

Thus the weight registered by machine is W = 360 N

Explanation:

We are given that:

Mass of man = 60 Kg

Angle "θ" = 60°

macosθ + mgcosθ = N

N = 60 x 2 x 1/ 2 + 60 x 10 x 1/2

N = 60 + 60 x 5

N = 60 + 300

N = 360 N

Thus the weight registered by machine is W = 360 N