A concrete slab of mass 400 kg accelerates down a concrete slope inclined at 35°. The u kinetic bn the slab and slope is 0.60. Determine the acceleration of the block.
I do not care how massive the block is.
I do care the g = about 9.81 m/s^2
Force down slope = m g sin 35
normal force = m g cos 35
friction force up slope = 0.60 m g cos 35
so
m g ( sin 35 - 0.60 cos 35) = m a
a = g (sin 35 - 0.60 cos 35)
M*g = 400 * 9.8 = 3920 N. = Wt. of slab,
Fp = 3920*sin35 = 2248.4 N. = Force parallel to incline,
Fn = 3920*Cos35 = 3211 N. = Normal force,
Fk = u*Fn = 0.6 * 3211 = 1927 N. = Force of kinetic friction,
Fp-Fk = M*a,
2248.4 - 1927 = 400*a.
a=g(sin 35 -0.060 cos 35) =0.829
ROFL :)
determine the acceleration of the block.
Acceleration 400kg 35%
To determine the acceleration of the block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
In this problem, the force causing the slab to accelerate down the slope is the component of gravity parallel to the slope. This force can be calculated using the formula F = m * g * sin(θ), where m is the mass of the slab, g is the acceleration due to gravity, and θ is the angle of the slope.
First, let's calculate the force acting on the slab. We know that the mass of the slab is 400 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the angle of the slope is 35°.
F = m * g * sin(θ)
= 400 kg * 9.8 m/s^2 * sin(35°)
Now, let's calculate the net force. Due to friction, there will be a force that opposes the motion of the slab, which is the kinetic friction force. The formula for kinetic friction force is F_friction = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. The normal force is equal to the force perpendicular to the slope, which can be calculated using N = m * g * cos(θ).
Substituting the values, we have:
F_friction = μ * N
= μ * m * g * cos(θ)
= 0.60 * 400 kg * 9.8 m/s^2 * cos(35°)
Now, we can calculate the net force acting on the slab by subtracting the frictional force from the force applied parallel to the slope:
Net Force = F - F_friction
Finally, we can use Newton's second law (F = m * a) to solve for the acceleration:
m * a = Net Force
a = Net Force / m
Substitute the values and solve for acceleration.