A box is initially at rest on an inclined plane tilted at angle theta with respe

Question

A box is initially at rest on an inclined plane tilted at angle theta with respect to the horizontal. The box is attached by a low-mass, non-stretching rope to a freely-hanging mass. A uniform gravitational field g acts vertically downward. The pully is low-mass and frictionless. Given the information below determine: How much static friction is required to prevent the system from accelerating? What direction is this friction? What is the maximum possible static friction? Will the system accelerate when released from rest? If it does accelerate, what is the kinetic friction (magnitude and direction), and what is the acceleration (magnitude and direction)? What is the magnitude of the tension in the rope?

Explanation / Answer

Here,

1) for the static friction required

static friction required = mhanging * g - mbox * g * sin(theta)

static friction required = 3.11 * 9.8 - 3.82 * 9.8 * sin(62)

static friction required = -2.57 N

the static friction required is 2.57 N

2)

maximum static friction = us * m * g * cos(theta)

maximum static friction = 0.460 * 3.82* 9.8 * cos(62)

maximum static friction = 8.08 N

3)

the system will stay in rest

as the frictional force needed is less than the maximum possible friction

4)

It does not acceleration

5)

tension in rope = mhanging * g

tension in rope = 3.11 * 9.8

tension in rope = 30.5 N

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