Answer to Question #193934 in Classical Mechanics for Mike

Question

A 15 g bullet traveling parallel to an inclined ramp strikes a 2.74 kg block of wood and becomes imbedded in it. The impact drives the block a distance of 26 cm up the ramp. The ramp is inclined at 28°, and the coefficient of friction is 0.40. What is the speed of the bullet just before impact?

Answer 1

$\frac{mv^2}{2}=(m+M)gh+Nl,$

$\frac{mv^2}{2}=(m+M)gl\sin \alpha+\mu (m+M)gl\cos\alpha,$

$v=\sqrt{\frac{(m+M)gl(\sin\alpha+\mu \cos\alpha)}{m}}=19.6~\frac ms.$