A million dollar basic physics questions - if can take the challenge - then test your ability!!?

Question

At the same time a block of iron and an equally heavy iron sphere are released from the top of a slope. Assume that the friction between the slope has a negligible effect on the velocity of the block and the sphere. Which of the two will be down first?

There is this slope prepared for this experiment. Then a block of iron and equally heavy iron sphere is brought to the top of the slope and release from the top of the slope at the same time. OK – assuming that the friction between the slope has a negligible effect on the velocity of the block and the sphere – [who in yahoo answer has the intelligence to tell which of the two will be down first?]

** - very important show your working with answer

Answer 1

In the absence of friction both objects reach at the same time.

The only forces acting are 1) Weight 2) Normal reaction
The net force tangential to the incline = mg*sinθ
Thus the net acceleration = g*sinθ
This is independent of the mass (assuming that you neglect friction and air resistance).

In the absence of friction, the sphere will slide without rolling because all the forces act through its center. So rotational inertia has nothing to do with it.

*EDIT*
If there is friction, then depending on the coefficient of friction, the sphere may roll without sliding. If that is the case, then the sphere will have a higher acceleration than the block which slides.
It can be shown that the sphere will roll without sliding if
μ > 2/7 * tanθ
Without sliding, a = 5/7 * g*sinθ
With sliding, a = g*cosθ - μ*g*sinθ < 5/7 * g*sinθ

Answer 2

If there is no friction, then the block will descend the slope first. Why? Because the circumference of the rolling sphere will describe a cycloid as it rolls down the slope, and the direction of travel of any point on that circumference will therefore, during part of each revolution, be AWAY from the foot of the slope, and the overall speedof the sphere will be less than the block, all points of which will travel in a straight line.
Edit: I see Dr D's answer, but I assume that if there IS tro be adifference, it can only occur if the sphere rolls.

Answer 3

If there is no friction then the fact that the block has more surface area by volume than a sphere will have no effect. The difference in shape will also have no effect as they will both slide. There is no friction then there is no force to cause the sphere to roll /spin. They would both reach the bottom at equal speed in equal time.

Answer 4

buddy! this is a very simple question.Torque applied on the sphere at the point of contact by gravity is not balanced by the torque due since the torque due to friction is zero.So,at the point of contact the net torque will not be zero.So,there will be pure translational motion.So,they will fall simultaneously.

Answer 5

So:
1. Same mass
2. Same change in height
3. No friction, resistance etc?

Therefore... same kinetic energy at the bottom... and hence the same terminal velocity.

I say they reach the bottom at the same time.