Please be legible on paper (if provided) and please explain each steps. The spee

Question

Please be legible on paper (if provided) and please explain each steps.

The speed of a rifle bullet may be measured by means of a ballistic pendulum in the following way. The bullet, of known mass m and unknown speed v, embeds itself in a stationary wooden block of mass M, suspended as a pendulum of length L. This sets the block to swinging. The amplitude x of swing may be measured and. using conservation of energy, the velocity of the block immediately after impact may be found. Assume that x L. Show that the speed of the bullet is given by

Explanation / Answer

m*v = (m+M)*V

v = (m+M)*V / m......(1)

L^2 = x^2 +(L-h)^2

L^2 = x^2 +L^2 + h^2 - 2*h*L

2*h*L - h^2 = x^2

h is samaller than L ... h^2 is neglected

h = x^2/2L

0.5*(m+M)*V^2 = (m+M)*g*h = (m+M)*g*x^2/2L

V = x*sqrt(g/L)

rom 1'

v =((m+M)/m)*(x*sqrt(g/L))

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