Question

A) Determine the acceleration of a 25.0 kg mass down a frictionless incline plane (angle of incline=30 degrees)

B) Repeat the above problem for an incline with a coefficient of friction of 0.15.

Answer 1

(A) Mass of the object, m = 25.0 kg

Angle of inclination, = 30 deg

When you will draw the free-body-diagram of the object, you will find that the downward acceleration of the object is the component of gravitational acceleration 'g' along the inclined plane.

Since the surface is frictionless the opposing force will be zero.

Therefore, acceleration of the object, a = g*sin

= 9.8*sin30

= 9.8*0.5 = 4.9 m/s^2 (Answer)

(B) Coefficient of friction of the incline, = 0.15

So, the frictional force opposing the motion = *m*g*cos

So, the net force along the inclined plane, F = m*g*sin -  *m*g*cos

Therefore, acceleration of the object, a = F/m = g*sin -  *g*cos

= 9.8*sin30 - 0.15*9.8*cos30

= 9.8*0.5 - 0.15*9.8*0.866

= 4.9 - 1.27 = 3.63 m/s^2 (Answer)