# Homework Help: Find force to push block up incline with static and kinetic friction in certain time

1. Jul 27, 2012

### hairE

p1. The problem statement, all variables and given/known data
A 5.03 box sits at rest at the bottom of a ramp that is 8.76 long and that is inclined at 30.0 above the horizontal. The coefficient of kinetic friction is 0.40, and the coefficient of static friction is 0.50.

What constant force , applied parallel to the surface of the ramp, is required to push the box to the top of the ramp in a time of 4.45 ?

2. Relevant equations
max mu_static * force Normal = Force to budge Block
mu_kinetic * force Normal = Force Friction

3. The attempt at a solution

The force to overcome the static friction is what is confusing me.
To start: Find acceleration.
8.76m / 4.45 s = 1.969 m/s = veloc.
1.969 m/s /4.45 s = .4425 m/s^2 = accel.

F= ma = 5.03*.4425 = 2.225 N = Leftover, or net force to keep the block accelerating up the ramp

(Parallel to plane) ƩF= Push - Force static - force kinetic - Weight = 2.25N
2.25N = Push - mgsin(30) - (mu_k)mgcos(30) - (mu_s)mgcos(30)

BUT*** Force static is only acting until the object budges. And the question is asking for a CONSTANT force applied. I'm confused. PLEASE help!!! I just need the sum of forces explained to me.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 27, 2012

### Staff: Mentor

Re: Find force to push block up incline with static and kinetic friction in certain t

Either static or kinetic friction acts--not both (at the same time).

Since the object is moving, use kinetic friction. (Will the calculated force be enough to overcome static friction?)

3. Jul 27, 2012

### TSny

Re: Find force to push block up incline with static and kinetic friction in certain t

Hi HairE
Are you clear as to what velocity you just calculated? Is it the velocity at some particular time during the motion or is it the overall average velocity? With that in mind, are you sure you calculated the acceleration correctly?

4. Jul 27, 2012

### Staff: Mentor

Re: Find force to push block up incline with static and kinetic friction in certain t

Oops... TSny is right.
You'll need to redo this calculation. (In addition to what I already pointed out.)

5. Jul 27, 2012

### CWatters

Re: Find force to push block up incline with static and kinetic friction in certain t

Humm. If the coefficient of static friction is higher than the kinetic friction presumably you have to apply a force at least strong enough to get it moving. Then check that force gets it up the ramp quick enough. If not then even more force is required.