Physics: Newton's Laws Problems

[kingwinner]

I am badly stuck on a few Newton's Laws problems. I hope someone can help me out! Thanks a million! :eek:

 

1) A 5 kg block rests on a 30 degrees incline. The coefficient of static friction between the block and incline is 0.20. How large a horizontal force must push on the block if the block is to be on the verge of sliding

1a) up the incline?

1b) down the incline?

 

I really have no clue of solving this. Would 1a and 1b have the same answer?

 

2) A double incline plane has two boxes of equal masses on opposite sides connected by a rope over a pulley. The left incline is 53 degrees and the right incline is 30 degrees. The coefficient of static and dynamic friction are equal, 0.30 for both boxes.

2a) Show that the system, when released, remains at rest.

2b) If the system is given an initial speed of 0.90m/s to the left, how far will it move before coming to rest?

 

For 2a, I know that the motion of attempted of the system is to the left beucase the left incline is steeper and the boxes have equal masses. So there are 2 frictional forces, both pointing to the right. Knowing all these, I got that the acceleration is 0.69441m/s^2

. Then, how can the system remain at rest? Can someone explain? I don't understand.

 

For 2b, v1=-0.90m/s, v2=0, a=0.69441. Using these, I found that the system moves 0.58m to the left before coming to rest. But can I use the acceleration that I got in part a? Is this the correct way of doing it?

 

3) The radius of the earth is about 6370km, while that of Mars is 3440km. If an object weights 200N on earth, what would it weight, and what would be the acceleration due to gravity, on Mars? Mars has a mass 0.11 that of earth.

 

I tried using law of universal gravitation equation and it works. I am wondering if there is any way of solving this problem without the use of the law of universal gravitation beucase this equation is not taught in my course yet.

[Jay-qu]

for 1 you have to resolve the forces in a common direction - since gravity pulls straight down and friction acts at an angle of 30 degrees. once you have resolved the forces so they are in the same (or 90 degree) directions you just use vector addition. 1a and 1b wont have the same answer, this is an easy thought experiment - you have something resting on an incline, is it easier to push up or down?

[kingwinner]

1) "you have something resting on an incline, is it easier to push up or down?"

But in this case, you are not actually pushing down the box, right? In both 1a and 1b, your applied force is in the direction up the slope, so in both cases you are pushing up.

 

And for both 1a and 1b, the box is at rest and the acceleration is 0, right? Then the frictional force points up the slope in both cases because its attempted motion in both cases is sliding down. So wouldn't the applied force required be the same for 1a and 1b?

[Jay-qu]

your getting there.. The bit about been easier to push up and down was an extra question i was asking only loosely related to the question.

 

Yes the accel. will be 0 in both but the force is in opposite directions, so you have to work out the forces - hint *friction opposes motion or potential motion*

[kingwinner]

I think I got question 1!

 

Question 2 is really weird. I got a=0.69441m/s^2 for part a, which means that the system is accelerating in the direction

, but how is that possible? The left incline is steeper......

[Jay-qu]

ok just going through the maths as I do this..

 

mg*sin[53] - 0.30(mg*cos[53]) - T + T - mg*sin[30] - 0.30(mg*cos[30]) = ma

 

that is how i would do it but doesnt mean it is correct - the friction there is the max. friction - it doesnt have to be that.

[kingwinner]

ok just going through the maths as I do this..

 

mg*sin[53] - 0.30(mg*cos[53]) - T + T - mg*sin[30] - 0.30(mg*cos[30]) = ma

 

that is how i would do it but doesnt mean it is correct - the friction there is the max. friction - it doesnt have to be that.

2a) But when I work it out, I got a=0.69441m/s^2

indeed. What solid, firm argument can I place to refute this answer and state that the acceleration is 0m/s^2?

 

Is it true that friction can't cause acceleration in the same direction as the frictional force? (as in this case, friciton is acting to the right, so it is not possible for the system to accelerate to the right??)

 

But when a person is walking, its free body diagram has three forces, including a foward reaction force in the direction of acceleration? (and that is frictional force, right?)

[Jay-qu]

It is because 0.30N is the max frictional force. Imagine pushing against a box of very large mass of say 100kg with a coefficient of friction of 0.3 it would have a max frictional force of 294N - so this doesnt mean if you push it with 100N then it will push 194N back! it will only push 100N back and will not move

:cry: I hope this clears some questions up..