Amy is in a tuck and skiing straight down a 30° slope. Air resistance pushes backward on her with a force of 10 N. The coefficient of dynamic friction between her skis and the snow is 0.08. Amy’s mass is 60 kg. What is the resultant of the external forces that act on Amy?
To find the resultant of the external forces acting on Amy, we need to consider the forces of gravity, air resistance, and friction.
1. Calculate the force of gravity:
The force of gravity acting on Amy can be calculated using the formula:
Force of gravity = mass * acceleration due to gravity
Given that Amy's mass is 60 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force of gravity:
Force of gravity = 60 kg * 9.8 m/s^2 = 588 N
2. Calculate the force of friction:
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction * normal force
The normal force can be calculated using the formula:
Normal force = mass * gravitational acceleration * cosine(theta)
where theta is the angle of the slope.
Given that the coefficient of dynamic friction is 0.08, the gravitational acceleration is 9.8 m/s^2, and the angle of the slope is 30 degrees, we can calculate the normal force and the force of friction:
Normal force = 60 kg * 9.8 m/s^2 * cos(30°) = 514.6 N
Force of friction = 0.08 * 514.6 N = 41.2 N
3. Calculate the net external force:
The net external force is the vector sum of all the external forces, which in this case are the force of gravity, air resistance, and friction. Since the force of air resistance pushes backward, while the force of gravity and friction act downward, we can calculate the net external force as follows:
Net external force = Force of gravity - Force of air resistance - Force of friction
Net external force = 588 N - 10 N - 41.2 N = 536.8 N
Therefore, the resultant of the external forces acting on Amy is 536.8 N.
To find the resultant of the external forces acting on Amy, we need to analyze the forces acting on her.
First, we need to determine the force due to gravity. The force due to gravity can be calculated using the formula:
Force due to gravity (Fg) = mass (m) x gravity (g)
Given that Amy's mass is 60 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the force due to gravity:
Fg = 60 kg x 9.8 m/s² = 588 N
Next, we need to calculate the force due to friction. The force due to friction can be calculated using the formula:
Force due to friction (Ff) = coefficient of friction (μ) x normal force (Fn)
Since Amy is skiing straight down the slope, the normal force is equal to the component of the force due to gravity that is perpendicular to the slope. The normal force can be calculated using the formula:
Normal force (Fn) = Fg x cos(θ)
where θ is the angle of the slope, which in this case is 30°.
Fn = 588 N x cos(30°) = 588 N x 0.866 = 509.808 N
Now we can calculate the force due to friction:
Ff = 0.08 x 509.808 N = 40.78464 N (approximately 40.8 N)
Lastly, we need to consider the force of air resistance which pushes backward on Amy with a force of 10 N. Since this force is already given, we can simply include it in the analysis.
Now we can find the resultant of the external forces acting on Amy by summing up the individual forces and vector quantities:
Resultant force = Force due to gravity + Force due to friction + Force of air resistance
Resultant force = 588 N + 40.8 N + 10 N
Resultant force = 638.8 N
Thus, the resultant of the external forces that act on Amy is approximately 638.8 Newtons.