Q 81

Expert-verifiedFound in: Page 291

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A 20 kg wood ball hangs from a 2.0-m-long wire. The maximum tension the wire can withstand without breaking is 400 N. A 1.0 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the greatest speed this projectile can have without causing the wire to break?

The greatest speed that projectile can have without causing the wire to break is 90.3 ms^{-1}

We need to find out the the greatest speed that this projectile can have without causing the wire to break.

v_{pi} and v_{f} denotes the initial velocity of the projectile and the final velocity of the ball embedded with the projectile respectively.

After collision, the projectile with ball moves in a circular arc.

Using the Principle of conservation of momentum,

m_{p}v_{pi} = (m_{p} + m_{b})v_{f}

To find v_{pi} , the value of v_{f} is required

After collision, the ball with projectile moves in a circular arc.

The force acting along wire is given as

Centripetal force is also acting due to the wire. Therefore,

And it is calculated that

v_{pf} = 21v_{f}

Therefore,

v_{pf }=

v_{pf }= 90.3 ms^{-1}

Hence, The greatest speed that projectile can have without causing the wire to break is 90.3 ms^{-1}

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