Question

In: Physics

A 3 kg box sits on a ramp where the coefficient of friction is 0.3. Find...

A 3 kg box sits on a ramp where the coefficient of friction is 0.3. Find the angle that will cause the box to slide downhill at constant velocity.

Hints:

constant velocity means a = 0

sum the forces (downhill pull and friction) and solve for θ

sin θ / cos θ = tan θ

take the arctan

Expert Solution

Gravitational acceleration = g = 9.81 m/s²

Mass of the box = m = 3 kg

Angle of the ramp =

Normal force on the box from the ramp = N

Coefficient of friction = = 0.3

Friction force on the box = f

f = N

The box is moving at constant velocity therefore the acceleration of the box is zero that means all the forces on the box are balanced.

From the free body diagram,

N = mgCos

f = mgCos

f = mgSin

mgCos = mgSin

= Tan

Tan = 0.3

= 16.7^o

Angle of the ramp that will cause the box to slide at constant velocity = 16.7^o

genius_generous answered 10 months ago

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