Question

A ball of mass m is released from rest from q height H along a smooth tube having a semicircular portion so that the ball just reaches the top of the semicircular. (a) Find the radius of the semicircular. (b) Find the maximum force imparted by the ball on the ground.​

Answer 1

Answer:

ular. (a) Find the radius of the semicircular. (b) Find the maximum force imparted by the ball on the ground

Answer 2

Solution :-

(a) Since the ball moves inside the tube, it can stay at the top of the tube with zero speed.

=> VB = 0

$Applying \: COE \: principal , \frac{1}{2} m \: \\ (Vc {}^{2} - VB {}^{2} ) - mg(2r) = 0$

$Putting \: VB = 0 \: and \: Vc = \sqrt{2gH}$

$We \: obtain, => r = \frac{ H}{2}$

(b) At the lowest position C, let the (maximum) thrust exerted on the ground be N.

$N-mg = mar = \frac{mv^2 c}{r}$

$=> N = m[ \frac{V^2c}{r} + g]$

where Vc can be obtained by conserving energy between A and C as

$\frac{1}{2} mv {}^{2} c - mg \: H = 0 = > V {}^{2} c = 2g H$

$=> N = m [ \frac{( \sqrt{(2gH) {}^{2} } }{r} + g]$

$Putting \: r = \frac{H}{2} , we \: obtain,$

$N = m [ \frac{ 2 gH}{H/2 + g} ] = 5mg.$

Explanation:

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