A concrete slab of mass 400 kg accelerates down a concrete slop inclined at 35degree. The kenetic friction b/n the slab and slope is 0.60.Determine the acceleration of block.

8.02

force down: mg*sinTheta

friction up: mg*mu*cosTheta

net force=mass*acceleration
mg*(SinTheta-mu*CosTheta)=ma
solve or a.

A slab on a slop.

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8.02

0.082

8.02

To determine the acceleration of the concrete slab, we will first calculate the force components that are affecting its motion.

1. Find the force of gravity on the slab:
The force of gravity (weight) can be calculated using the formula:
Weight = mass × gravity

Given:
mass = 400 kg
gravity = 9.8 m/s² (approximate value)

Weight = 400 kg × 9.8 m/s² = 3920 N

2. Calculate the force component parallel to the incline:
The force component parallel to the incline is the force of gravity (weight) multiplied by the sin of the angle of the slope.

Force_parallel = Weight × sin(slope angle)
Force_parallel = 3920 N × sin(35°) ≈ 2246 N

3. Calculate the force component perpendicular to the incline:
The force component perpendicular to the incline is the force of gravity (weight) multiplied by the cos of the angle of the slope.

Force_perpendicular = Weight × cos(slope angle)
Force_perpendicular = 3920 N × cos(35°) ≈ 3198 N

4. Determine the force of kinetic friction:
The force of kinetic friction can be calculated by multiplying the coefficient of kinetic friction (µ) with the perpendicular force component.

Force_friction = µ × Force_perpendicular
Given: kinetic friction coefficient (µ) = 0.60

Force_friction = 0.60 × 3198 N ≈ 1919 N

5. Calculate the net force acting on the slab:
The net force is the difference between the force parallel to the incline and the force of kinetic friction.

Net_force = Force_parallel - Force_friction
Net_force = 2246 N - 1919 N = 327 N

6. Apply Newton's second law of motion:
The net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Net_force = mass × acceleration

Rearranging the formula, we get:

acceleration = Net_force / mass

Substituting the values:

acceleration = 327 N / 400 kg ≈ 0.8175 m/s²

Therefore, the acceleration of the concrete slab down the slope is approximately 0.8175 m/s².