11. Momentum & Impulse

(I) In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile (of the same mass) causes the pendulum to swing twice as high, h₂ = 5.2 cm. The second projectile was how many times faster than the first?

(II) A 28-g rifle bullet traveling 190 m/s embeds itself in a 3.1-kg pendulum hanging on a 2.4-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s maximum displacement.

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?

(II) A pendulum consists of a mass M hanging at the bottom end of a massless rod of length ℓ, which has a frictionless pivot at its top end. A mass m, moving horizontally as shown in Fig. 9–44 with velocity v, impacts M and becomes embedded. What is the smallest value of v sufficient to cause the pendulum (with embedded mass m) to swing clear over the top of its arc?

A ballistic pendulum consists of a $4-\mathrm{kg}$ wooden block suspended from a string. A bullet of mass $0.05 \mathrm{kg}$ is fired horizontally into the block and becomes embedded in it. If the combined block and bullet rise to a height of $0.20 m$ after the collision, what was the initial speed of the bullet?