hint: for the ball to reach the ground without hitting the rock, the condition is that the y-coordinate of ball should be greater than a certain height.
placing the origin at the center of sphere, ##R^2=x^2+y^2##
##(x,y)## are coordinates on the surface of hemisphere
use kinematic...
The x-direction used is clearly along the ramp with positive direction going up along the ramp, I hope you are not confused about how the x-y coordinate system is defined in the given solution. You might want to draw a free body diagram to clear things up. When you take component of forces along...
It's about the places of error, here the error doesn't exist in the thousand's place. Hundred's place is uncertain in spite of the fact that it is significant!
I hope this helps!
Edit: It always helps to write in scientific notation...usually after rounding off its written as...
Your solution seems fine for "work done by you". "work done by friction" would be negative of the calculated value. Also note that your answer should have only two significant figures. That means answer should have been ##2.0~kJ##. This could be the reason you were marked down.
That assumption isn't correct. The given velocity in the question is the initial velocity. And it stops after 6 seconds. Acceleration would be negative. And it seems you did take that into account in the final equation, otherwise the answer wouldn't be correct. Yes, the answer is correct. But be...
no problem!...just to make it seem reasonable you can use ##v=v_{0}+a.t##, solving for time gives ##10~seconds##. It doesn't stop immediately, it slowly decelerates therefore time is comparatively large and so is the distance. I hope this makes more sense now!
does it?...check your final equation, you have done the rest of it correctly...it should be -ve because of deceleration (retardation), it just shows acceleration acts in direction opposite to its initial velocity
##0=6+2a##
##a=-3##
Edit: I think it was a typo, but this is what the equation is...
time would depend on the initial net acceleration. It would help if you draw free body diagram and check the net force acting on body. Would the net force depend on slope of incline?.---------->The correct answer to this question would answer your question.
Caution: They all will have same...
I believe its the "bearing" term that is the cause of problem. I quote Wikipedia :
what haruspex meant was that direction of velocity of A and displacement vector from A to B has angle zero between them. I hope this helps!
yeah, my mistake for overlooking that!...edited the original post...thanks for pointing that out!...btw I meant backward but wrote forward the rest of it was correct...silly me!:redface:
But you get the point, the ball will eventually start to roll. If translation kinetic energy is high...
That relation is only valid for pure rolling (no sliding). You shouldn't calculate torque about ICR, if the body is accelerating (remember what I said previously about fictitious torque).
friction in this case(back spin case) would be kinetic. and after a while if friction is present then...