As shown below, a bullet of mass m and speed v is fired at an at rest

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As shown below, a bullet of mass m and speed v is fired at an at rest sphere. The bullet goes through the sphere, and exits with a speed of v/2. The sphere is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the sphere.)

As shown below, a bullet of mass m and speed v is fired at an at rest sphere. The bullet goes through the sphere, and exits with a speed of v/2. The sphere is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the sphere.)

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As shown below, a bullet of mass

m

and speed

v

is fired at an at rest sphere. The bullet goes through the sphere, and exits with a speed of

\frac{v}{2}

. The sphere is attached to a rigid pole of length

L

and negligible mass. What is the minimum value of

v

such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary:

m, L, g

, and

M

for the mass of the sphere.) (i)

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$As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.536)v after passing through the target. (a) Before collision (b) After collision The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.443)KEbBC ] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) V = v M = m$

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$As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.536)v after passing through the target. (a) Before collision (b) After collision The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.443)KEb BC ] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) V = v M = m$

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