What is the minimum applied force required to ball up a ramp?

[biochemnerd]

View attachment ball up ramp.bmp

Homework Statement

1.A 75kg ball is dragged along a 12m ramp in order to get from the ground to the top of the ramp, which is 2m above ground. Determine the minimum applied force required if the frictional force acting on the ball (due to the ramp) is 75N.

m=75kg
d=12m
h=2m

Homework Equations

W=Fapp(d)
W=mgh

The Attempt at a Solution

*assuming no friction*:
W=mgh
w=75*9.8*2
W=1470 J (no friction)

...this is where I'm lost, i assume that the mass of the ball, and the fact that there is 75N have some correlation within the problem, but i think I've hit a rut. any ideas? (see attachment for diagram) any help is appreciated

 

[radou]

Why exactly did you find the work? Think about what you need to find.

 

[biochemnerd]

i'm just not sure what to do, because i can't find the Fnet (theres no acceleration mentioned), and i don't know which equations to used in this circumstance.

should i assume that since the mass of the ball is 75kg, and the fricional forces is 75N, that anything over 75N will be the minimum applied force? I'm not very confident in the question.

 

[radou]

should i assume that since the mass of the ball is 75kg, and the fricional forces is 75N, that anything over 75N will be the minimum applied force? I'm not very confident in the question.

OK, that's the first step. Now, you have three forces acting on the ball. Friction, gravity, and the force which will move the ball up. Any ideas on how to proceed?

 

[dvyu]

the fact that there is not acceleration means that the Fnet = 0

 

[radou]

the fact that there is not acceleration means that the Fnet = 0

You don't need to worry about acceleration.

You need to find the minimum force for which the system won't be in the state of equilibrium.

Think of the problem in terms of equilibrium.

 

[biochemnerd]

ok, so, considering:
Ff=75N
Fn/Fg=735 N
Fapp=?

am i to add the forces up to get a Fnet, then find Fapp?(which i assume won't work, because Fg and Fn cancel out, so the Fnet would =75N, or that of friction). I'm not clear as to my next step should be.any hint?

 

[radou]

ok, so, considering:
Ff=75N
Fn/Fg=735 N
Fapp=?

am i to add the forces up to get a Fnet, then find Fapp?(which i assume won't work, because Fg and Fn cancel out, so the Fnet would =75N, or that of friction). I'm not clear as to my next step should be.any hint?

You're looking at the forces in the direction of the hill. You have friction, one component of gravity, and the force you need to find.

 

[biochemnerd]

if it were a FBD, then Ff= -75N, so i can assume that as long as Fapp is greater than 75N (so it won't equal 0), then 76N is going to be sufficient? i don't know. :(

 

[radou]

if it were a FBD, then Ff= -75N, so i can assume that as long as Fapp is greater than 75N (so it won't equal 0), then 76N is going to be sufficient? i don't know. :(

Again, friction is not the only force. Your force has to be greater than the sum of friction and the component of gravity acting in the direction of friction.

Btw, 75.001 would be sufficient too, so you better use inequalities later on.

 

[biochemnerd]

Ff+Fg=Fapp
(-75)+(735)=Fapp
Fapp=660N

i feel like I'm missing something. so Fapp must be greater than 660N?
should i look at friction as Kinetic Friction? aaah

 

[radou]

Ff+Fg=Fapp
(-75)+(735)=Fapp
Fapp=660N

i feel like I'm missing something. so Fapp must be greater than 660N?
should i look at friction as Kinetic Friction? aaah

You're considering gravity wrong. You should take the component Fg*sin(A), where A is the angle between the hill and the horizontal ground.