Push - Push Away!

Classical Mechanics Level 4

Andrew want's to send a heavy ball A A from point P P to point Q Q . Andrew applies a constant force F F which is always parallel to the tangent at that point. The surface is smooth. He want's to do the least possible work. Find the height till which Andrew has to push the ball.

Round off answer to 2 decimal places.

Details And Assumptions :

  • Take height of point P = 0 P=0 .
  • Mass of ball A A is 2 M 2M .
  • F = 6 M g π F = \displaystyle \dfrac{6Mg}{\pi}
  • The curve is Quarter of a Circle with Radius is 20 m


The answer is 10.00.

Rajdeep Dhingra by Rajdeep Dhingra , 20, India

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1 solution

Aryan Goyat
Feb 13, 2016

F × X 360 × 2 π × R = 2 M g R F \times \frac{X}{360} \times 2\pi \times R = 2MgR
On solving we get X = 60 ∘ X = {60}^{\circ}
So height would be h = 20 − 20 cos ⁡ ( 60 ∘ ) = 10 h = 20 - 20\cos({60}^{\circ}) = \boxed{10}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I have edited the Latex. Can you confirm that the solution remains the same ?

Rajdeep Dhingra - 5 years, 4 months ago

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yep :) it is the same

aryan goyat - 5 years, 4 months ago

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Great! :-)

Rajdeep Dhingra - 5 years, 4 months ago

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