Calculating Friction & Coefficient: 0.50 kg Block on 30° Ramp

[runningirl]

Homework Statement

A block of mass 0.50 kg slides down a 30 degree ramp.

a) What force of friction opposes the motion of the block in order to make the acceleration equal to 2.0 m/s/s?

b) What coefficient of friction is necessary in order to accomplish this?

Homework Equations

f=ma

The Attempt at a Solution

net force=(9.8*.5)*sin30

2.45=.5(a)
a=4.9 m/s/s?

 

[venkatg]

Horizontal component of weight is mgsin(30) = 0.5mg
normal component = mgcos(30) = sqrt(3) * mg/2

0.5mg - F = ma

So F = 0.5mg - ma, we found F

Also F = mu * sqrt(3) * mg/2

mu = F/(sqrt(3) * mg/2)

 

[jmb88korean]

Use F=ma to find the force needed. a is 2 and m is 0.5. Then break the black's force of gravity into components qith trig. Subtract the force from F=ma from the force going down the ramp to get frictional force. The difference between the forces must be from friction. Simply find the normal force and use F(friction)= F(normal)(coefficient of friction)