For full points I need to see the work and a correct answer. Thank you. A projec

Question

For full points I need to see the work and a correct answer.

Thank you.

A projectile of mass 50.0 grams hits a wooden block suspended from a thin steel wire as shown. The mass of the thin wire can be ignored. The mass of the block is 2.00 kg. Assume that the projectile embeds itself in the block, and that the projectile is traveling horizontally at v (m/s) when it hits the block. The angle through which the wire swings before the block comes to rest for the first time is measured as 10.0 degree . The distance between the point of suspension of the wire and the center of mass of the block (the point within the block through which all its weight appears to act) is 2.00 m. Calculate v, the speed with which the projectile hits the block.

Explanation / Answer

With the 10 degree angle, we can find how highthe system goes

cos(10) = x/2

x = 1.9696 m

The height is 2 - 1.9696 = .03038 m

Now, through conservation of energy, PE = KE

mgh = .5mv^2

(9.8)(.03038) = .5(v^2)

v = .772 m/s

Finally conservation of momentum

(.05)(v) = 2.05(.772)

v = 31.6 m/s

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