A block slides from rest from the top of a plane 8m long and inclined 35o with the horizontal. If the coefficient of friction is 0.20, find how long it will take the body to reach the bottom of the plane.

component of weight down plane

= m g sin 35

friction up plane = .2 m g cos 35

so force accelerating m down plane
= m g (sin 35 - .2 cos 35)

a = force/m = g(sin 35 - .2 cos 35)

distance =(1/2) a t^2 = 8 meters
solve for t

I see your other problems. They are really just like this one. Try them.

I still don't get it sorry

To find the time it takes for the block to slide down the inclined plane, we can use the equations of motion. We'll divide the motion into two components: parallel and perpendicular to the incline.

1. Perpendicular Component:
The force acting perpendicular to the incline is the weight of the block. The weight can be calculated using the formula: weight = mass * gravity, where gravity is approximately 9.8 m/s^2.

The weight is given by the formula:
weight = mass * gravity

2. Parallel Component:
The force acting parallel to the incline is the component of the weight that is directed down the incline and the friction force. The friction force can be calculated using the formula: friction force = coefficient of friction * normal force.

The friction force is given by the formula:
friction force = coefficient of friction * weight * cos(theta), where theta is the angle of the incline.

3. Net Force:
The net force acting on the block parallel to the incline is the force that accelerates the block downward. It is calculated by subtracting the friction force from the component of the weight directed down the incline.

net force = weight * sin(theta) - friction force

4. Acceleration:
To calculate the acceleration, we can use Newton's second law "F = m*a", where F is the net force acting on the block parallel to the incline, m is the mass of the block, and a is the acceleration.

5. Time:
To find the time, we can use the equation of motion "s = v0*t + (1/2)*a*t^2", where s is the distance traveled, v0 is the initial velocity (which is zero in this case), and t is the time.

The distance traveled down the incline is equal to the length of the plane, which is 8m. So we can rewrite the equation as:

8 = (1/2)*a*t^2

We can rearrange this equation to solve for t:

t^2 = (16/a)
t = sqrt(16/a)

Now we have the expression for the time it takes for the block to reach the bottom of the plane.

To find the acceleration:

1. Calculate the weight of the block using the formula weight = mass * gravity, where gravity is approximately 9.8 m/s^2.
2. Calculate the friction force using the formula friction force = coefficient of friction * weight * cos(theta).
3. Calculate the net force using the formula net force = weight * sin(theta) - friction force.
4. Calculate the acceleration using the formula net force = mass * acceleration.
5. Substitute the value of acceleration into the equation of motion t = sqrt(16/a) to find the time.