Question

A 75 kg box slides down a 25.0 degrees ramp with an acceleration of 3.60 m/s/s.
1. Find the Mk between the box and ramp
2. What acceleration would a 175kg box have on this ramp?

show clearly

Answer 1

1. We have
ma=mg sin⁡α-μ_k mg cos⁡α=mg(sin⁡α-μ_k cos⁡α )
a=g(sin⁡α-μ_k cos⁡α )
a/g=sin⁡α-μ_k cos⁡α
μ_k=1/cos⁡α (sin⁡α-a/g)
μ_k=1/cos⁡25 (sin⁡25-3.6/9.8)=0.0610
2. The acceleration doesn’t depend on mass of the box. Thus, the acceleration will be the same:
a=3.60 m/s^2 .