Question

While a roofer is working on a roof that slants at 45.0 ∘ above the horizontal, he accidentally nudges his 88.0 N toolbox, causing it to start sliding downward, starting from rest. If it starts 4.50 m from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof if the kinetic friction force on it is 18.0 N ?

Answer 1

Angle =45⁰

Force =88 N

Kinetic friction Force=18 N

Find _k,

Assume g=9.81m/s²

Frictional force=88_kcos(45^o)=18 Here we can assume a rotated coordinate system

k=0.29

Change in force, dF=mgsin(45^o)−_kmgcos(45^o)=ma

Cancel m on both side

a=gsin(45^o)−kgcos(45^o)=6.72

We know that ,v²=u²+2a(x)

v²=2(6.72)(4.5)=60.5

v=7.779 m/s