A 41g bullet is traveling at 499m/s when it strikes a block of wood. If the block of wood exerts a force of 50,000 N opposing the motion of the bullet, how far will the bullet penetrate the block of wood?
0.17meter
To find out how far the bullet will penetrate the block of wood, we will use the principle of work done. The work done on the bullet is equal to the force applied multiplied by the distance over which the force is applied.
The work done on the bullet can be expressed as:
Work = Force x Distance
Now, we need to rearrange this equation to solve for the distance (D):
Distance = Work / Force
In this case, the force opposing the motion of the bullet is 50,000 N, and the work done on the bullet can be calculated using the formula:
Work = Change in Kinetic Energy
The change in kinetic energy (ΔKE) is given by:
ΔKE = 1/2 x mass x (final velocity^2 - initial velocity^2)
Considering the given information, the initial velocity (u) of the bullet is 499 m/s, and the final velocity (v) is assumed to be 0 m/s (since the bullet comes to a stop upon hitting the wood block). The mass (m) of the bullet is given as 41 g, which can be converted to kg by dividing it by 1000:
m = 41 g / 1000 = 0.041 kg
Now, we can calculate the change in kinetic energy (ΔKE) as follows:
ΔKE = 1/2 x 0.041 kg x (0^2 - 499^2)
ΔKE = -1/2 x 0.041 kg x 499^2
ΔKE = -0.5 x 0.041 kg x 499^2
ΔKE = -0.5 x 0.041 kg x 249,001
ΔKE = -510.02 J
Since the work done on the bullet is equal to the change in kinetic energy, we can substitute the values into the equation for work:
Work = -510.02 J
Finally, we can substitute the values of work and force into the formula to calculate the distance:
Distance = Work / Force
Distance = -510.02 J / 50,000 N
Distance ≈ -0.0102 m
The negative sign indicates that the bullet will stop before it penetrates the block of wood. Hence, the approximate distance the bullet will penetrate the block of wood is 0.0102 meters before coming to a stop.