A 64 kg skier is on a 18 degree slope. The coefficient of kinetic friction between the skis and snow is .04. A) What is the weight of the skier? B) what is the normal force of the slope on the skier? C) why is the “parallel” force on the skier? D) what is the frictional force on the skis? E) what is the acceleration of the skier? F) how fast will the skier be going after 3.2 seconds?

a. mg

b. mgCosTheta
c. why? Because of gravity
d. mg*mu*cosTheta
e. in the parallel direction:
net force=ma
mg*sinTheta-mg*mu*CosTheta=m*a solve for acceleration a
f. vf=a*t^2

weight = m g = 64*9.81 = 628 Newtons

normal force = 628 cos 18 = 597 Newtons

parallel force = 628 sin 18 = 194 Newtons

mu * normal force = .04*597 = 24 Newtons

total force down slope=194-24= 170 Newtons
so a = F/m = 170/64 = 2.65 m/s^2
(check that is about .27 g which is a bit less than 9.81 sin 18 because of the friction)

v = a t if initial speed is zero
v = 2.65 * 3.2

vf = a t

Prof Damon is right on F, the world series kept me up late last night.

A) To find the weight of the skier, we need to use the formula weight = mass * gravity. The acceleration due to gravity is approximately 9.8 m/s². Therefore, the weight of the skier is:

Weight = mass * gravity = 64 kg * 9.8 m/s² = 627.2 N

B) The normal force is the force exerted by the surface perpendicular to the skier's motion. On an inclined slope, the normal force can be determined using the formula:

Normal force = weight * cos(angle)

In this case, the angle is 18 degrees. Therefore:

Normal force = 627.2 N * cos(18°) ≈ 603.38 N

C) The "parallel" force on the skier refers to the component of the skier's weight that acts parallel to the slope. It is given by the equation:

Parallel force = weight * sin(angle)

Parallel force = 627.2 N * sin(18°) ≈ 178.68 N

D) The frictional force on the skis can be calculated using the formula:

Frictional force = coefficient of friction * normal force

In this case, the coefficient of kinetic friction is 0.04. Thus:

Frictional force = 0.04 * 603.38 N ≈ 24.14 N

E) To find the acceleration of the skier, we need to consider the net force acting on the skier in the direction of motion. This can be calculated using the equation:

Net force = parallel force - frictional force

Net force = 178.68 N - 24.14 N = 154.54 N

Next, we use the formula:

Net force = mass * acceleration

Rearranging the formula to solve for acceleration:

Acceleration = Net force / mass = 154.54 N / 64 kg ≈ 2.42 m/s²

The acceleration of the skier is approximately 2.42 m/s².

F) To find how fast the skier is going after 3.2 seconds, we can use the equation:

Final velocity = Initial velocity + (acceleration * time)

Since we don't know the initial velocity, we assume it is zero since the skier starts from rest:

Final velocity = 0 + (2.42 m/s² * 3.2 s) ≈ 7.75 m/s

Therefore, after 3.2 seconds, the skier will be traveling at approximately 7.75 m/s.