Answer :
Final answer:
a) The friction acting on the piano from the ramp is 115.14 N.
b) The acceleration of the piano down the ramp is 3.89 m/s².
Explanation:
To determine the friction acting on the piano from the ramp, we can use the formula:
f_kinetic = μk × N,
where f_kinetic s the kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force.
The normal force can be calculated by taking the component of the weight of the piano perpendicular to the incline, which is:
N = mg × cosθ,
where m is the mass of the piano and g is the acceleration due to gravity. So,
f_kinetic = 0.119 × (114 kg × 9.8 m/s² × cos(30°)).
f_kinetic = 115.14 N
To find the acceleration of the piano down the ramp, we can use the formula:
a = (Fnet - f_kinetic) / m,
where Fnet is the net force acting on the piano, f_kinetic is the frictional force, and m is the mass of the piano. The net force can be calculated by taking the component of the weight of the piano parallel to the incline, which is:
Fnet = mg × sinθ.
So,
a = (114 kg × 9.8 m/s² × sin(30°) - f_kinetic) / 114 kg.
a = (114 kg × 9.8 m/s² × sin(30°) - 115.14 N) / 114 kg.
a = 3.89 m/s²
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