A bullet of 10g enters a target at 100 ms-1 and leaves it 0.01 s later. Calculate:
i. The rate of change of momentum of the bullet
ii. The resistance offered by the target
iii. The loss of kinetic energy of the bullet
iv. The deceleration of the bullet
v. The distance travelled by the bullet in passing through the target
At what speed does the bullet leave the target?
More information is needed.
To calculate the various quantities, we need to apply the principles of momentum and energy conservation. Let's go step by step:
i. The rate of change of momentum of the bullet:
The rate of change of momentum is given by the formula Δp/Δt, where Δp is the change in momentum and Δt is the time taken.
Δp = m * (v_f - v_i)
Here, m = mass of the bullet = 10g = 0.01 kg (since 1 kg = 1000g)
v_i = initial velocity of the bullet = 100 m/s
v_f = final velocity of the bullet = 0 m/s (since the bullet comes to rest)
Δt = time taken = 0.01 s
Δp = 0.01 kg * (0 - 100 m/s) = -1 kg⋅m/s (the negative sign indicates the change in direction of momentum)
So, the rate of change of momentum is -1 kg⋅m/s or 1 N⋅s.
ii. The resistance offered by the target:
The resistance offered by the target can be determined using Newton's third law which states that every action has an equal and opposite reaction. The resistance offered by the target is equal and opposite to the force exerted by the bullet on the target.
Therefore, the resistance offered by the target is also 1 N.
iii. The loss of kinetic energy of the bullet:
The loss of kinetic energy can be determined using the formula ΔKE = (1/2) * m * ((v_f)^2 - (v_i)^2)
Here, m = mass of the bullet = 0.01 kg
v_i = initial velocity of the bullet = 100 m/s
v_f = final velocity of the bullet = 0 m/s
ΔKE = (1/2) * 0.01 kg * ((0 m/s)^2 - (100 m/s)^2)
= (1/2) * 0.01 kg * (-10000 m^2/s^2)
= -500 J (negative sign indicates the loss of kinetic energy)
iv. The deceleration of the bullet:
Deceleration is the rate at which velocity decreases. It can be calculated using the formula:
a = (v_f - v_i) / Δt
Here, v_i = 100 m/s and v_f = 0 m/s, and Δt = 0.01 s (time taken to stop)
a = (0 m/s - 100 m/s) / 0.01 s
= -10000 m/s^2 (negative sign indicates deceleration)
v. The distance travelled by the bullet in passing through the target:
To calculate the distance travelled, we need to determine the average velocity, which is given by:
v_avg = (v_i + v_f) / 2
v_avg = (100 m/s + 0 m/s) / 2
= 50 m/s
Now, the distance traveled is given by d = v_avg * Δt
d = 50 m/s * 0.01 s
= 0.5 m
So, the bullet travels a distance of 0.5 meters while passing through the target.