A 30-gram bullet leaves a gun barrel with a speed of 230 m/s. (a) What work is done on the bullet while it is in the gun barrel? (b) If the gun is 0.60m long, what is the average force on the bullet?
work = 1/2 m v^2
Vf^2=1/2 a * distance, where acceleration a= force/mass, solve for force.
a)W = KE = 1/2 mv^2
b)F = W/d
To find the work done on the bullet while it is in the gun barrel, we can use the formula for work:
Work = Force x Distance
Since the gun barrel only exerts a force on the bullet while it is in contact with it, we can assume that the force acting on the bullet is constant. Therefore, the work done can be calculated by multiplying the force by the distance traveled by the bullet in the gun barrel.
(a) Work done on the bullet:
Given:
Mass of the bullet (m) = 30 grams = 0.03 kg
Speed of the bullet (v) = 230 m/s
We know that work (W) is equal to the change in kinetic energy. Since the bullet starts from rest in the gun barrel, the initial kinetic energy is zero. Therefore, the work done on the bullet is equal to its final kinetic energy.
Kinetic energy (K.E.) = (1/2) x mass x velocity^2
K.E. = (1/2) x 0.03 kg x (230 m/s)^2
Now we can calculate the work done:
Work = K.E.
(b) To find the average force on the bullet, we can use the formula:
Average Force = Work / Distance
Given:
Length of the gun barrel (d) = 0.60 m
Now we can calculate the average force on the bullet:
Average Force = Work / Distance
It's important to note that this calculation assumes that the force on the bullet is constant throughout its travel within the gun barrel. In reality, the force may vary due to factors such as friction.