ENGINEERING PRINCIPLES – BET105
TUTORIAL 5: FRICTION and ELASTICITY
01.
Take the positive x direction as up the slope. For max acceleration,
Net Fx = ma = f - wx = 1/2 µmgcosØ – mgsinØ
So the maximum acceleration is, a = g(1/2 µcosØ – sinØ)
a). On dry concrete,
µ = 1.00
a = (9.8ms-2)(1/2 x 1 x cos40 – sin40)
a = 4.2ms-2
b). On wet concrete,
µ = 0.700
a = (9.8ms-2)(1/2 x 0.7 x cos40 – sin40)
a = 2.74ms-2
c). On ice,
µ = 0.100
a = (9.8ms-2)(1/2 x 0.1 x cos40 – sin40)
a = - 0.195ms-2
The negative sign indicates downwards acceleration, so the car cannot make it up the grade.
02.
F = Y(ΔL/Li)A
W = mg
4360 = 210 x 109 (ΔL/610)(0.707)
W = (72+400)9.8
4360 = 2.43 x 107 ΔL
W = 4360N
ΔL = 0.191mm
A = πr2
A = 0.0707