Answer :
Final answer:
The skier's acceleration is determined by the net force acting on them (force of gravity minus friction). Using values given and formulas for various forces (gravitational and frictional), we can calculate that the skier's acceleration is approximately 1.94 m/s^2 downhill.
Explanation:
The subject of this question is Physics, specifically the branch known as mechanics. The problem states: 'An 84 kg skier glides down a 20° incline hill, with a coefficient of kinetic friction of 0.15.'
To solve this, firstly, one must calculate the force of gravity acting on the skier along the path of the hill. This force depends on the mass of the skier, the acceleration due to gravity, and the angle of the hill. It can be calculated using the formula Fgravity = m * g * sin(θ), where m is the mass, g is the acceleration due to gravity (~9.81 m/s^2), and θ is the angle of the hill.
- So, Fgravity = 84 kg * 9.81 m/s^2 * sin(20°) = about 281.8 N.
Next, calculate the force of kinetic friction that resists the motion of the skier. This force is calculated as f = μN, where μ is the coefficient of kinetic friction, and N is the normal force - which in this case, due to the angle of the hill is m*g*cos(θ).
- So, N = m * g * cos(θ) = 84 kg * 9.81 m/s^2 * cos(20°) = about 790.2 N.
- Then f = μN = 0.15 * 790.2 N = 118.5 N.
Finally, we can find the net force acting on the skier (Fnet) which will be the force of gravity minus the force of friction and calculate the acceleration (a), using the formula a = Fnet/m.
- So Fnet = Fgravity - f = 281.8 N - 118.5 N = 163.3 N
- Then a = Fnet / m = 163.3 N / 84 kg = about 1.94 m/s^2 downhill.
Learn more about Physics of Skiing here:
https://brainly.com/question/10595258
#SPJ11
