Figure shows a small block of mass m = 1 kg which is given a horizontal velocity v 0 = 10 m / s on the horizontal part of the bigger block of mass M = 9 kg placed on a horizontal floor. The curved p

Question

Figure shows a small block of mass m = 1 kg which is given a horizontal velocity v 0 ​ = 10 m / s on the horizontal part of the bigger block of mass M = 9 kg placed on a horizontal floor. The curved part of the surface shown is semicircular of radius R = 1 m . Find the distance (in m ) from point B where the block m lands finally after looping the semicircular part BCD. Neglect friction everywhere. Assume that the horizontal portion AB is long enough. ( g = 10 m / s 2 )

TestHub · Accepted Answer

Let v r ​ be the block's velocity relative to the bigger block at the highest point and v the bigger block's velocity; the small block's ground velocity is v r ​ − v . Momentum: m v 0 ​ = M v − m ( v r ​ − v ) ⇒ 10 v − v r ​ = 10 . Energy: 2 1 ​ m v 0 2 ​ = 2 m g R + 2 1 ​ M v 2 + 2 1 ​ m ( v r ​ − v ) 2 ⇒ 9 v 2 + ( v r ​ − v ) 2 = 60 . Solving: v r ​ = 7.5 m/s. Flight time: t = g 2 × 2 R ​ ​ = 0.632 s; BE = v r ​ t = 7.5 × 0.632 = 4.74 m

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