Abullet of mass m is fired into a block of mass m that is at rest. the block, with the bullet embedded, slides distance d across a horizontal surface. the coefficient of kinetic friction is ? k.
part a
find an expression for the bullet's speed vbullet.
part b
what is the speed of a 9.0 g bullet that, when fired into a 12 kg stationary wood block, causes the block to slide 5.4 cm across a wood table? assume that ? k=0.20.

A. The bullet's speed is [ ( M + m ) / m ] √ ( 2 μ g d )

B. The initial speed of the 9.0 g bullet is about 610 m/s

Let's recall Impulse formula as follows:

where:

I = impulse on the object ( kg m/s )

∑F = net force acting on object ( kg m /s² = Newton )

t = elapsed time ( s )

Let us now tackle the problem!

Given:

mass of bullet = m = 9.0 g = 9.0 × 10⁻³ kg

mass of block = M = 12 kg

sliding distance = d = 5.4 cm = 5.4 × 10⁻² m

coefficient of kinetic friction = k = 0.20

Asked:

initial bullet's speed = u₁ = ?

Solution:

Firstly, we will use Conservation of Energy formula to find the speed of the block:

→ Equation A

Next, we will use Conservation of Momentum formula to find the initial speed of the bullet:

← Equation A

Grade: High School

Subject: Physics

Chapter: Dynamics

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