To find the magnitude of the acceleration of the sled as it moves up the slope, we need to consider the forces acting on the sled.
1. The force of gravity (Fg) can be divided into two components:
- The component perpendicular to the slope (Fg⊥), which is equal to mg * cos(θ), where m is the mass of the sled and g is the acceleration due to gravity (9.8 m/s^2).
- The component parallel to the slope (Fg∥), which is equal to mg * sin(θ).
2. The force of friction (Ff) is given by the coefficient of kinetic friction (μk) multiplied by the normal force (Fn), where Fn = mg * cos(θ).
3. The net force (Fnet) acting on the sled up the slope is given by the difference between the parallel component of the force of gravity and the force of friction:
Fnet = Fg∥ - Ff
4. The acceleration (a) of the sled is given by Newton's second law of motion:
Fnet = ma
Substituting the values into the equations, we can calculate the magnitude of the acceleration:
Fg⊥ = mg * cos(θ) = m * 9.8 * cos(5.00°)
Fg∥ = mg * sin(θ) = m * 9.8 * sin(5.00°)
Fn = mg * cos(θ)
Ff = μk * Fn
Fnet = Fg∥ - Ff
ma = Fnet
Now we can calculate the values step by step.