at on time, the velocity of a rifle bullet was measured using a ballistic pendulum made up of a wooden block suspended from a string. the block used here has a mass of 20kg. a 50g rifle bullet is fired into the block, penetrating it by 10cm and causing it to swing upwards, increasing its height by 20cm.
a) calculate the velocity of the bullet as it enters the wooden block. Express you answer in km/h.
b) calculate the frictional force between the bullet and the wooden block.
Use conservation of energy (GPE=KEinitial) to find the velocity of the block/bullet at impact. Then, use conservation of momentum to find the initial velocity of the bullet at impact.
the work done by the bullet can be determined by energy:
KE of block/bullet-friction*.10m=KE bullet initial.
To calculate the velocity of the bullet as it enters the wooden block, we can use the principle of conservation of momentum. This principle states that the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system. In this case, the bullet and the wooden block are the only objects involved, so we can calculate the velocity of the bullet before it entered the wooden block using the following formula:
m1v1 = (m1 + m2)v2
Where:
m1 = mass of the bullet = 50g = 0.05kg
v1 = velocity of the bullet before entering the block
m2 = mass of the wooden block = 20kg (given)
v2 = velocity of the bullet and block after the collision
We need to convert the unit of velocity from m/s to km/h in the final answer.
a) Now, let's calculate the velocity of the bullet before it entered the wooden block:
m1v1 = (m1 + m2)v2
0.05kg * v1 = (0.05kg + 20kg) * v2
v1 = ((0.05kg + 20kg) * v2) / 0.05kg
v1 = (20.05kg * v2) / 0.05kg
Since we don't have the value of v2 yet, we need to determine it from the given information about the wooden block's swing. The change in height of the block is given as 20cm, and the block's mass is 20kg. We can use the concept of conservation of mechanical energy to relate the initial kinetic energy of the bullet and block system to the potential energy when the block reaches its maximum height. The equation is as follows:
mgh = (1/2)(m1 + m2)v2²
Where:
m = mass of the wooden block = 20kg
g = acceleration due to gravity = 9.8 m/s²
h = change in height = 20cm = 0.20m
m1 = mass of the bullet = 50g = 0.05kg
v2 = velocity of the bullet and block after the collision
Simplifying and rearranging the equation, we can solve for v2:
v2 = sqrt((2 * mgh) / (m1 + m2))
v2 = sqrt((2 * 20kg * 9.8 m/s² * 0.20m) / (0.05kg + 20kg))
Now that we have the value of v2, we can substitute it back into the equation for v1:
v1 = (20.05kg * v2) / 0.05kg
By plugging in the values and performing the calculations, we can find the velocity of the bullet as it enters the wooden block.