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.

a) 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

Gravitational acceleration = g = 9.81 m/s2

Weight of the toolbox = W = 88 N

Mass of the toolbox = m

W = mg

88 = m(9.81)

m = 8.97 kg

Angle of slant of the roof = = 45 degrees

Distance of the lower edge of the roof from the initial position of the toolbox = L = 4.5 m

Height the toolbox falls through = H

H = LSin

Kinetic friction force on the toolbox = f = 18 N

Speed of the toolbox when it reaches the edge of the roof = V

The initial potential energy of the toolbox is converted into the kinetic energy of the toolbox at the edge of the roof plus the energy lost against friction.

V = 6.66 m/s

a) Speed of the toolbox when it reaches the edge of the roof = 6.66 m/s