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/

M*g = 8 * 9.8 = 78.4 N. = Wt. of block.

Fp = 78.4*sin40 = 50.4 N. = Force parallel to the incline.

Fn = 78.4*cos40 = 60.1 N. = Normal force

Fk = u*Fn = 0.35 * 60.1 = 21 N. = Force
of friction.

a = (Fp-Fk)/M = (50.4-21)/8 = 3.68 m/s^2

d = 0.5a*t^2 = 0.5*3.68*3^2 = 16.54 m.

To determine how far the block travels in 3 seconds, we need to break down the problem into several steps:

1. Determine the force of gravity acting on the block:
The force of gravity can be calculated using the formula: F = m * g, where m is the mass of the block (8kg) and g is the acceleration due to gravity (9.8 m/s^2). So, F = 8 kg * 9.8 m/s^2 = 78.4 N.

2. Determine the force of friction:
The force of friction can be calculated using the formula: F_friction = μ * F_normal, where μ is the coefficient of kinetic friction (0.35) and F_normal is the normal force. The normal force can be calculated as F_normal = m * g * cos(θ), where θ is the angle of inclination (40 degrees). So, F_normal = 8 kg * 9.8 m/s^2 * cos(40°) = 63.18 N. Thus, F_friction = 0.35 * 63.18 N = 22.12 N.

3. Determine the acceleration of the block:
The net force acting on the block can be calculated as the difference between the force of gravity and the force of friction: F_net = F - F_friction = 78.4 N - 22.12 N = 56.28 N. Using Newton's second law, F_net = m * a, we can solve for the acceleration (a): 56.28 N = 8 kg * a, so a = 7.04 m/s^2.

4. Determine the distance traveled:
To calculate the distance traveled by the block in 3 seconds, we can use the formula: d = v_0 * t + 0.5 * a * t^2, where v_0 is the initial velocity (0 m/s), t is the time (3 seconds), and a is the acceleration (7.04 m/s^2). Simplifying the equation, we have: d = 0 * 3 + 0.5 * 7.04 m/s^2 * (3 s)^2 = 0 + 0.5 * 7.04 m/s^2 * 9 s^2 = 28.16 m.

Therefore, the block travels a distance of 28.16 meters in 3 seconds.