A(n) 15 g bullet is fired into a(n) 116 g block
of wood at rest on a horizontal surface and
stays inside. After impact, the block slides
15 m before coming to rest.
The acceleration of gravity is 9.8 m/s
2
.
If the coefficient of friction between the
surface and the block is 0.7, find the speed of
the bullet before impact.
Answer in units of m/s
The kinetic energy of the (bullet+block) after impact equals the work done against friction at the point where it stops. Solve for the velocity right after impact, V'. Then use conservatiuon of momentum to solve for the bullet velocity, V.
(1/2)(m+M) V'^2 = (m+M)*Mu*g*X
V' = 14.35 m/s
m*V = (m+M)*V'
What does the M in Mu stand for in the equation? Momentum?
To find the speed of the bullet before impact, we can use the principles of conservation of momentum and work-energy theorem.
First, let's determine the initial momentum of the bullet-block system. The initial momentum (p) is given by:
p = m bullet * v bullet
where m bullet is the mass of the bullet and v bullet is the speed of the bullet before impact.
The bullet is fired into the block and stays inside. This means that the impulse (change in momentum) experienced by the system is zero. The impulse (J) is given by
J = m block * Δv
where m block is the mass of the block and Δv is the change in velocity of the block.
Since the block was initially at rest, the change in velocity (Δv) is equal to the final velocity (v) of the block. Therefore,
J = m block * v
The impulse is also related to the work done on the block by friction (W):
J = W
The work done is equal to the force of friction (F friction) multiplied by the distance over which it acts (d). The force of friction can be calculated as:
F friction = μ * (m block * g)
where μ is the coefficient of friction between the surface and the block, and g is the acceleration due to gravity.
Therefore, we have:
J = F friction * d
m block * v = μ * (m block * g) * d
Now, we can solve for v:
v = (μ * g * d) / m block
Substituting the given values:
μ = 0.7
g = 9.8 m/s^2
d = 15 m
m block = 116 g = 0.116 kg
v = (0.7 * 9.8 * 15) / 0.116
Calculating this, we find that the speed of the bullet before impact is approximately 91.09 m/s.