1) While a roofer is working on a roof that slants at 40.0 above the horizontal,
ID: 1402805 • Letter: 1
Question
1) While a roofer is working on a roof that slants at 40.0 above the horizontal, he accidentally nudges his 86.0 Ntoolbox, causing it to start sliding downward, starting from rest.
If it starts 4.35 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 22.0 N ?
2) A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces a potential energyU(x) given by U(x)= x4 where =1.15 J/m4 .
What is the force when the particle is at position x = -0.570 m ?
Explanation / Answer
1)
mass of the toolbox, m = W/g = 86/9.8 = 8.78 kg
Net force acting on the toolbox,
Fnet = m*g*sin(40) - kinetic friction
m*a = m*g*sin(40) - 22
a = g*sin(40) - 22/m
= 9.8*sin(40) - 22/8.78
= 3.8 m/s^2
now use kinematic equation.
v^2 - u^2 = 2*a*d
v^2 - 0^2 = 2*a*d)
= sqrt(2*3.8*4.35)
= 5.37 m/s <<<<<<<-------------Answer
2) Fx = -dU/dx
= -alfa*4*x^3
at x = -0.57 m
Fx = -1.15*4*(-0.57)^3
= 0.852 N <<<<<<<-------------Answer
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