Find force to push block up incline with static and kinetic friction in certain time

[hairE]

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Homework Statement

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 ?

Homework Equations

max mu_static * force Normal = Force to budge Block
mu_kinetic * force Normal = Force Friction

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.

 

[Doc Al]

(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)

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?)

 

[TSny]

Hi HairE

8.76m / 4.45 s = 1.969 m/s = veloc.

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?

 

[Doc Al]

Oops... TSny is right.

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.

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

 

[CWatters]

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.