Final answer:
The acceleration of a 10.0-kg mass sliding down a 25.0-degree incline with a coefficient of kinetic friction of 0.520 is approximately 0.123 m/s².
Step-by-step explanation:
The student has asked about the acceleration of a 10.0-kg mass sliding down a 25.0° incline given the coefficients of static and kinetic friction.
Firstly, we must identify the forces involved. The gravitational force component acting down the slope is mg sin θ, where m is the mass, g is the acceleration due to gravity (9.8 m/s2), and θ is the angle of the incline. The kinetic frictional force, which opposes the motion, is μk mg cos θ, with μk as the coefficient of kinetic friction.
Net force down the slope (Fnet) is the difference between the gravitational force component and the kinetic frictional force:
- Fnet = mg sin θ - μk mg cos θ
We then use Newton's second law (F = ma) to calculate the acceleration (a):
- a = Fnet / m
- a = (g sin θ - μk g cos θ)
- a = (9.8 sin 25° - 0.520 * 9.8 cos 25°)
Calculating the values gives us:
- a = (4.115 - 0.520 * 8.889)
- a ≈ 0.123 m/s2
This is the acceleration of the 10.0-kg mass while it is sliding down the incline.