Will the Cart Roll Down the Hill Despite Friction?

[rawr8712]

Homework Statement

An 0.80-kg cart rolls down a 30.0° hill from a
vertical height of 0.50 m. The distance that the cart must roll to the bottom of
the hill is 0.50 m/sin 30.0°=1.0 m. The surface of
the hill exerts a frictional force of 5.0 N on the cart.
Does the cart roll to the bottom of the hill?

Homework Equations

I do know what equation to use or how to get the problem started.
f=ma

The Attempt at a Solution

F=9.8m/s^2(.8kg)
F=7.84N(sin30)
F=3.92N
so it doesn't over come the frictional force.

 

[tiny-tim]

Welcome to PF!

Homework Statement

An 0.80-kg cart rolls down a 30.0° hill from a
vertical height of 0.50 m. The distance that the cart must roll to the bottom of
the hill is 0.50 m/sin 30.0°=1.0 m. The surface of
the hill exerts a frictional force of 5.0 N on the cart.
Does the cart roll to the bottom of the hill?

Hi rawr8712! Welcome to PF!

Yes, the downhill component of gravity is 3.92N, so if the friction force is 5N, the cart will accelerate uphill!.

Are you sure you've copied the question accurately?​

 

[swmn2102]

Hi rawr8712! Welcome to PF!

Yes, the downhill component of gravity is 3.92N, so if the friction force is 5N, the cart will accelerate uphill!.

Are you sure you've copied the question accurately?​

the cart will not accelerate up the hill seeing as the force stated for friction is the maximum force that friction can exert not a constant. therefore the cart will not move