The figure above shows an object (blue) on top of a wedge (gray) sitting on a sc

Question

The figure above shows an object (blue) on top of a wedge (gray) sitting on a scale (black). When the object is released, is slides down the slope of the wedge. What is the normal force of the scale on the wedge (this is the force the scale will read) as the mass slides down the slope?

There is friction between the object and the wedge and between the wedge and the scale. The static friction between the wedge and the scale is large enough to keep the wedge from moving.

The mass of the object is 2.8 kg.

The mass of the wedge is 5.1 kg.

The angle of the wedge is 20 degrees.

The coefficient of kinetic friction between the object and wedge is 0.13.

Give your answer in Newtons and to three significant digits.

Explanation / Answer

Normal Force , N = m*g*cos(20)
Friction Force, F = u*m*g*cos(20)
Force of an object on the wedge, = m*g -  u*m*g*cos(20) * sin(20)

Normal force of the scale on the wedge , = M*g + m*g -  u*m*g*cos(20) * sin(20)
Normal force of the scale on the wedge , = 5.1*9.8 + 2.8*9.8 - 0.13 * 2.8*9.8 * cos(20)*sin(20)
Normal force of the scale on the wedge , = 76.3 N

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