Write an algebraic expression for the coefficient of kinetic friction for a block of mass m sliding down an incline of angle theta with respect to the horizontal with acceleration a. (type the formula out with the word (theta) for the angle. Make sure you are careful with your parentheses. You may use the following variables: m, a, g, (theta) and the sin, cos, and tan function

n = {gsin(theta) - a}/gcos(theta)

OR n = tan(theta) {at constant velocity}

Explanation:

For a block of mass m sliding down an incline at angle theta, the forces acting on the object along the plane are the moving force (down the plane) and the frictional force which is acting opposite the moving force (i.e acting up the plane).

The moving force Fm = Wsin theta where W is the weight of the block and theta is the angle of inclination.

The frictional force Ff is expressed as the product of the coefficient of kinetic friction (n) and the normal reaction force (R) acting on the body i.e Ff = nR

Since the body is accelerating down the plane, we will apply the Newton's second law to solve for the coefficient of the kinetic friction.

According to the law;

Force = mass × acceleration

F = ma... (1)

Summation of the force acting on the body along the plane will be;

Fm - Ff

= Wsin (theta) - nR

Since R =Wcos(theta), the sum of the forces becomes;

Wsin(theta) - n(Wcos(theta))

Since W = mg, the equation becomes;

mgsin(theta) - nmgcos(theta)... (2)

Substituting equation 2 into 1, we will have;

mgsin(theta) - nmgcos(theta) = ma

gsin(theta) - ngcos(theta) = a

ngcos(theta) = gsin(theta) - a

Dividing both sides by gcos(theta) to get n which is the coefficient of kinetic friction will give;

n = {gsin(theta) - a}/gcos(theta)

If the body moves with a constant velocity, acceleration 'a' will be zero and the coefficient of kinetic friction n will become;

n = {gsin(theta) - 0}/gcos(theta)

n = gsin(theta)/gcos(theta)

n = sin(theta)/cos(theta)

n = tan(theta)

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

where is the photo and the answer choices?