A bullet of mass 200 grams is forced with work speed of 400 m/s of it is stopped in 100 m,
Find:
a.) KE
b.) Force needed to stop it
To find the kinetic energy (KE) of the bullet, we can use the formula:
KE = (1/2) * mass * velocity^2
a.) KE = (1/2) * 0.2 kg * (400 m/s)^2
= 0.04 kg * 160000 m^2/s^2
= 6,400 Joules
So, the kinetic energy of the bullet is 6,400 Joules.
b.) To find the force needed to stop the bullet, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be represented as:
Work = Change in KE
The work done to stop the bullet is equal to the force applied multiplied by the distance over which the force is applied. Mathematically, it can be represented as:
Work = Force * Distance
Since the bullet is being stopped, the work done is equal to the negative change in kinetic energy. Therefore, we can write:
-Change in KE = Force * Distance
To find the force, we rearrange the equation:
Force = -Change in KE / Distance
To calculate the change in kinetic energy, we use the initial kinetic energy (KEi) minus the final kinetic energy (KEf):
Change in KE = KEf - KEi
Since the bullet comes to a stop, the final kinetic energy (KEf) is 0 (zero). Therefore:
Change in KE = 0 - KEi
= -KEi
Substituting the values into the equation for force:
Force = -(-KEi) / Distance
= KEi / Distance
Hence, the force needed to stop the bullet is:
Force = 6,400 Joules / 100 m
= 64 Newtons
Therefore, the force needed to stop the bullet is 64 Newtons.