Question

A 20.0 kg box slides 1.60 m down a rooftop with a 30.0° incline and a coefficient of kinetic friction of 0.342. It then falls off the rooftop and hits the ground. Assume no air resistance. The bottom of the rooftop is 2.78 m above ground.

What are the components of the weight, using axes parallel and perpendicular to the rooftop? Write the normal force and the force of friction in component form?

Answer 1

let a is the acceleration of the box.

net force acting on the box along the inclined surface,

Fnet = m*g*sin(theta) - fk

m*a = m*g*sin(theta) - N*mue_k

m*a = m*g*sin(theta) - m*g*cos(theta)*mue_k

a = g*sin(theta) - g*cos(theta)*mue_k

= 9.8*sin(30) - 9.8*cos(30)*0.342

= 2.0 m/s^2

now use, vf^2 - vi^2 = 2*a*d

vf = sqrt(2*a*d)

= sqrt(2*2*1.6)

= 2.53 m/s

parallel component of velocity = 2.53 m/s

perpendicular component of velocity = 0

Normal force = m*g*cos(theta) j

= 20*9.8*cos(30) j

= 170 j

kinetic frcition, fk = -m*g*cos(theta)*mue_k i

= -20*9.8*cos(30)*0.342 i

= -58.0 i