The 60.0 kg skier shown below is skiing down a 35.0 degree incline where the magnitude of the friction force is 38.5N
a. what is the acceleration of the skier?
b. what is the normal force on the skier?
Normal force = m g cos 35 {part B}
force down slope = m g sin 35 - 38.5
so
m a = m g sin 35 - 38.5
a = 9.81 sin 35 - (38.5/60) {part A}
To determine the acceleration of the skier, we need to consider the forces acting on the skier. In this case, there are two main forces: gravity and friction. The force of gravity is directed down the incline and can be divided into two components: the force parallel to the incline and the force perpendicular to the incline. The friction force opposes the motion of the skier and acts parallel to the incline.
a. To find the acceleration, we first need to calculate the net force acting on the skier. This can be done by subtracting the force of friction from the force parallel to the incline.
The force parallel to the incline is given by: F_parallel = m * g * sin(theta),
where:
m = mass of the skier (60.0 kg)
g = acceleration due to gravity (9.8 m/s^2)
theta = angle of the incline (35.0 degrees)
F_parallel = 60.0 kg * 9.8 m/s^2 * sin(35.0 degrees)
Next, we subtract the friction force from the force parallel to the incline to get the net force:
Net force = F_parallel - F_friction
Net force = (60.0 kg * 9.8 m/s^2 * sin(35.0 degrees)) - 38.5 N
Finally, we can use Newton's second law, F = m * a, to find the acceleration:
Net force = m * a
a = Net force / m
Substituting the values, we can calculate the acceleration.
b. The normal force on the skier can be found using the force perpendicular to the incline. The force perpendicular to the incline is given by:
F_perpendicular = m * g * cos(theta)
Substituting the values, we can calculate the normal force.
Let's calculate them step by step:
a. acceleration of the skier:
F_parallel = 60.0 kg * 9.8 m/s^2 * sin(35.0 degrees)
Net force = F_parallel - 38.5 N
a = Net force / m
b. normal force on the skier:
F_perpendicular = 60.0 kg * 9.8 m/s^2 * cos(35.0 degrees)
Now, let's calculate them.
To solve this problem, we need to break it down into smaller steps.
a. To find the acceleration of the skier, we need to start by calculating the net force acting on the skier. The net force is the vector sum of all the forces acting on the skier.
1. Start by determining the force component parallel to the incline. This force is composed of the gravitational force and the friction force. The gravitational force acting on the skier can be calculated using the formula Fg = mg, where m is the mass of the skier (60.0 kg) and g is the acceleration due to gravity (9.8 m/s^2).
Fg = 60.0 kg * 9.8 m/s^2 = 588 N
2. The friction force (Ff) is given as 38.5 N.
3. The force component parallel to the incline (F_parallel) is given by F_parallel = Fg - Ff.
F_parallel = 588 N - 38.5 N = 549.5 N
4. Next, find the acceleration (a) using the equation F_parallel = ma, where m is the mass of the skier.
a = F_parallel / m = 549.5 N / 60.0 kg = 9.16 m/s^2
Therefore, the acceleration of the skier is 9.16 m/s^2.
b. The normal force (Fn) is the force exerted by a surface to support the weight of an object resting on it. In this case, it counteracts the gravitational force acting on the skier perpendicular to the incline.
1. The normal force (Fn) can be calculated using the formula Fn = mg * cos(θ), where θ is the angle of the incline (35.0 degrees).
Fn = 60.0 kg * 9.8 m/s^2 * cos(35.0 degrees) = 490.2 N
Therefore, the normal force on the skier is 490.2 N.