An 60 kg skier is sliding down a ski slope at a constant velocity. The slope makes an angle of 13° above the horizontal direction.
(a) Ignoring any air resistance, what is the force of kinetic friction acting on the skier? in N
(b) What is the coefficient of kinetic friction between the skis and the snow?
Ws = mg = 60kg * 9.8N/kg = 588 N. = Wt.
of skier.
Fs = 588 N. @ 13 Deg. = Force of skier.
Fp = 588*sin13 = 132.3 N. = Force parallel to incline.
Fv = 588*cos13 = 572.9 N. = Force perpendicular to incline.
a. Fp -Fk = 0, Because a = 0.
132.3 - Fk = 0,
Fk = 132.3 N. = Force of kinetic friction.
b. u*Fv = Fk = 132.3 N,
u*572.9 = 132,3,
u = 132.3 / 572.9=0.232. = coefficient
of frictin.
THNKS :)
To calculate the force of kinetic friction acting on the skier, we can use the equation:
\( F_{friction} = \mu_k \times F_{normal} \),
where \( F_{normal} \) is the normal force and \( \mu_k \) is the coefficient of kinetic friction.
(a) First, let's determine the normal force acting on the skier. The normal force is usually equal to the weight of the object when it is on a horizontal surface. However, in this case, the ski slope is inclined at an angle of 13°. The normal force can be calculated using the equation:
\( F_{normal} = m \times g \times \cos(\theta) \),
where \( m \) is the mass of the skier (60 kg), \( g \) is the acceleration due to gravity (9.8 m/s^2), and \( \theta \) is the angle of the slope (13°).
Substituting the values, we have:
\( F_{normal} = 60 \times 9.8 \times \cos(13°) \).
Calculating this expression, we find:
\( F_{normal} \approx 572.113 \, \text{N} \).
Now, let's calculate the force of kinetic friction using the equation mentioned above:
\( F_{friction} = \mu_k \times F_{normal} \).
We don't have the value of \( \mu_k \) yet, so we will solve equation (b) first and then substitute this value into the equation to find the force of kinetic friction.
(b) To find the coefficient of kinetic friction (\( \mu_k \)), we can use the equation:
\( \mu_k = \tan(\theta) \),
where \( \theta \) is the angle of the slope (13°).
Substituting the value of \( \theta \) into the equation, we have:
\( \mu_k = \tan(13°) \).
Calculating this expression, we find:
\( \mu_k \approx 0.228 \).
Now, substituting this value of \( \mu_k \) into the equation for the force of kinetic friction, we have:
\( F_{friction} = 0.228 \times 572.113 \).
Calculating this expression, we find:
\( F_{friction} \approx 130.55 \, \text{N} \).
To calculate the force of kinetic friction acting on the skier, we need to first determine the normal force acting on the skier. The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it.
(a) To find the normal force, we can use the equation:
Normal force = Weight (mg) * cos(angle)
In this case, the weight of the skier is given as 60 kg, and the angle of the slope is given as 13° above the horizontal direction. The acceleration due to gravity, g, is approximately 9.8 m/s².
Normal force = 60 kg * 9.8 m/s² * cos(13°)
Normal force ≈ 588 N
Since the skier is sliding down the slope at a constant velocity (meaning there is no acceleration), the force of kinetic friction is equal to the force of gravity in the opposite direction. Therefore, the force of kinetic friction is also 588 N.
(b) To find the coefficient of kinetic friction between the skis and the snow, we can use the equation:
Coefficient of kinetic friction = Force of kinetic friction / Normal force
In this case, the force of kinetic friction is 588 N (as calculated in part a) and the normal force is also 588 N.
Coefficient of kinetic friction = 588 N / 588 N
Coefficient of kinetic friction = 1
Therefore, the coefficient of kinetic friction between the skis and the snow is 1.