A 100 kg box lifes on a plank making an angle of teta with the horizontal.use a

Question

A 100 kg box lifes on a plank making an angle of teta with the horizontal.use a coordinates system where the x axis is parallel to the surface of the block and the yaxisperpenducular to it. What is the Normal force of the plank on the box? What is the x component of the weight If there is 0 friction, what would be the acceleration of the box? If p, = the coefficient static friction and the box does not slide, what is the x component of the friction force of the plank on the box? What then is the x component of the net force?And the box will just start to slide when Now suppose the box is sliding down the incline with acceleration , how does this relate to mu_k But if the box is sliding up the incline

Explanation / Answer

Here,

mass , m = 100 Kg

theta

1)

weight of box = m * g * cos(theta)(-j)

weight of box = -100 * 9.8 * cos(theta) j

weight of box = - 980 j N

2)

normal force on the box = - weight of box

normal force on the box = 980 j * cos(theta) N

3)

the x component of the force = - m *g * sin(theta) i

the x component of the force = -980 * sin(theta) i

4)

let the acceleration is a

Using second law of motion

m *a = - m *g * sin(theta) i

a = - 9.8 * sin(theta) i

the acceleration of the box is - 9.8 * sin(theta) i

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