An 8kg block starts from rest from the top of a plane, inclined at 40o with respect to the horizontal, and slides down at a

constant acceleration. If the coefficient of kinetic friction between the block the plane is 0.35 determine how far the
block travels in 3s.
2013/

constant acceleration....

down the plane: mgsinTheta
friction up the plane: mg*mu*cosTheta

Net force=ma
mg sinTheta-mg*mu*cosTheta=ma
a= g(sinTheta-muCosTheta)

find a, then

distance=1/2 a t^2 solve for distance

To determine how far the block travels in 3 seconds, we need to calculate the acceleration of the block first.

The force of gravity acting on the block can be divided into two components: one parallel to the plane (mg*sinθ) and one perpendicular to the plane (mg*cosθ). Here, θ is the angle of inclination, which is 40 degrees.

The force of friction acting on the block is given by: 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 perpendicular component of the weight, which is N = mg*cosθ.

The net force acting on the block parallel to the plane is: F_net = f_parallel - f_friction, where f_parallel = mg*sinθ and f_friction = μ * N.

Since the block is sliding down the plane, the net force is in the direction of motion, so we can write the equation of motion as: F_net = ma, where m is the mass of the block and a is the acceleration.

Substituting the values, we have: mg*sinθ - μ * mg*cosθ = ma

Simplifying the equation, we get: a = g * (sinθ - μ * cosθ)

Now we can calculate the acceleration using the given values: g = 9.8 m/s² (acceleration due to gravity), θ = 40°, and μ = 0.35.

a = 9.8 * (sin40° - 0.35 * cos40°)

Next, we can use the kinematic equation to find the distance traveled by the block in 3 seconds. The kinematic equation is: s = ut + 0.5at², where s is the distance, u is the initial velocity (which is zero in this case), t is the time, and a is the acceleration.

Substituting the values, we have: s = 0 + 0.5 * a * (3²)

Calculate the value of a and substitute it into the equation to find the distance traveled by the block in 3 seconds.