2 Quick Physis Questions?

Question

I need help getting started on these 2 problems. (Step by step instructions will definitely earn you 10 points)

1. A company truck is on its way to deliver a birthday cake for a birthday party when it rounds a curve with a radius 20.0 m at a speed of 12 m/s. What coefficient of friction is needed between the cake pan and the truck in order to keep the pan from slipping?

2. Steve's car rounds an unbanked curve that has a radius of 100 m. If the coefficient of friction between the tires and the road is 0.40, what is the fasted speed the car can round the curve without risking an accident?

Thanks!
-willm16

Answer 1

look up centripetal force and centrifugal force
Fcent=mv2/r.

Friction force = uN
where u is the coefficient of friction and N is the normal force (N = mg) mg assumes the surface remains horizontal. As soon as you bank, the normal force becomes a component normal to the surface, but your problems imply the road is flat/horizontal so N = mg.

Friction must equal centripetal force so nothing slides around.
Fcent = Friction
which (mv^2)/r = u(mg)
the m's cancel so you're left with (v^2)/r = ug

now you can solve for u (coefficient of friction) since you know v, r and g (9.81 meters/second^2) for problems 1 and 2.

Answer 2

Here are two very quick answers.
1.
Force of riction is
f=uN
F<=f where
F=ma and
a=V^2/R

mV^2/R<=umg

u>=V^2/(Rg)
u>= .733

2. Same relationship applies here
mV^2/R=umg
V=sqrt(ugR)
V=19.8m/s

Answer 3

x2*(a+b)a^x+x2+100(20^3*y+b)=75@intern5