High School

A 114 kg piano is placed on an incline plane of 300 in order to load it out of a moving truck .Without adding an applied force the piano is released to allow it to travel down the ramp.If there is a coefficient of kinetic friction of 0.119 determine a) The friction acting on the piano from the ramp b) The acceleration of the piano down the ramp.

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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