A bullet travelling with velocity of 100 ms-1 pierces a block of wood and moves with a velocity of 10 ms-1 . If the thickness of the block reduces to one half of the previous value, what wiil be the emerging velocity of the bullet?
Is this block of wood stationary ?
If so
loss of energy in block = F of friction time thickness
energy loss = (1/2)m (100)^2 - (1/2)m(10^2)
= (m/2)(9900)
If we only lost half as much then
(m/2)(100)^2 - (m/2)v^2 = (m/2)(4950)
v^2 = 5050
v = 71.1 m/s
To find the emerging velocity of the bullet, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
In this scenario, the bullet is initially traveling with a velocity of 100 m/s and pierces a block of wood, reducing its velocity to 10 m/s. Let's assume the mass of the bullet is "m" and the mass of the block of wood is "M".
The initial momentum of the bullet is given by:
Initial momentum = mass of the bullet × initial velocity of the bullet
Initial momentum = m × 100 m/s = 100m
The final momentum of the bullet after it pierces the block can be expressed as:
Final momentum = mass of the bullet × final velocity of the bullet
Final momentum = m × 10 m/s = 10m
Since the total momentum before and after the event is conserved, we can equate them:
Total initial momentum = Total final momentum
This gives us:
100m = 10m
Simplifying the equation, we find:
90m = 0
This implies that the mass of the bullet, "m", is zero. However, this is not physically possible. Therefore, there must be an external force acting on the bullet-block system, resulting in a change in momentum.
In the absence of any other information about the system or the external force, we cannot determine the emerging velocity of the bullet accurately.
the question was, what if the block of wood were only half as thick?
Anyway (assuming a constant deceleration), half the thickness means half as long spent decelerating, so the change in velocity will be only half as much, ending up with a speed of 55 m/s.