A bullet of mass of 30g and travelling at a speed of 200msˉ¹ embeds itself in a wooden block. The bullet penetrates a distance of 12cm into the wood. Using the concepts of work done by a force and kinetic energy, determine the average resistive force acting on the bullet.
Kinetic energy = work of resistive force
mv^2/2= W= F•s•cosα
cosα = 1
F= mv^2/2•s=0.03•(200)^2/2•0.12=5000 N
Kinetic energy = work of resistive force
mv^2/2= W= F•s•cosα
cosα = -1(α=180 deg.)
-F= mv^2/2•s=0.03•(200)^2/2•0.12=5000N
Well, this bullet is really getting into some deep woodwork! Let's see if we can calculate the average resistive force acting on it.
First, we need to calculate the initial kinetic energy of the bullet before it embeds itself in the wooden block. The formula for kinetic energy is KE = 0.5 * m * v^2, where m is the mass of the bullet and v is its velocity.
So, plugging in the values, we have KE = 0.5 * 0.03 kg * (200 m/s)^2.
Calculating that, we have KE = 0.03 * 200^2 = 600 J. (J stands for Joules, by the way, not jokes!)
Now, let's determine the work done by the resistive force. The formula for work done is W = F * d, where F is the force applied and d is the distance over which the force is applied.
The bullet penetrates a distance of 12 cm, which we need to convert to meters. So, 12 cm is 0.12 m.
Since we're looking for the average resistive force, we'll rearrange the formula to solve for force: F = W / d.
Substituting the values, we have F = 600 J / 0.12 m, which gives us F = 5000 N.
So, the average resistive force acting on the bullet is 5000 Newtons. That's quite a strong force to stop this bullet's adventure through the wood!
To find the average resistive force acting on the bullet, we need to use the concepts of work done by a force and kinetic energy.
1. First, let's find the initial kinetic energy of the bullet before it embeds itself in the wooden block.
The formula to calculate kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
- Mass of the bullet = 30 g = 0.03 kg
- Velocity of the bullet = 200 m/s
Plugging in these values into the formula:
Initial Kinetic Energy = (1/2) * 0.03 kg * (200 m/s)^2
2. Next, let's find the work done by the resistive force. The work done is equal to the change in kinetic energy.
The formula to calculate work is:
Work = Change in Kinetic Energy
Since the bullet embeds itself in the wooden block, the final kinetic energy is zero.
So, the change in kinetic energy = Initial Kinetic Energy - Final Kinetic Energy.
Change in Kinetic Energy = Initial Kinetic Energy - 0 (since final kinetic energy is zero)
3. Now, let's convert the distance penetrated by the bullet into meters.
Given:
- Distance penetrated by bullet = 12 cm = 0.12 m
4. We can relate the work done to the resistive force and distance using the formula:
Work = Force * Distance
Rearranging the formula, we get:
Force = Work / Distance
Substituting the values, we have:
Force = Change in Kinetic Energy / Distance
5. Now, let's calculate the average resistive force.
Force = Change in Kinetic Energy / Distance
Substituting the values:
Force = (Initial Kinetic Energy - 0) / 0.12 m
Calculate the initial kinetic energy using the formula from step 1, then substitute the value into the formula above.
After calculating, you will get the average resistive force acting on the bullet.
To determine the average resistive force acting on the bullet, we need to analyze the work done by the force acting against the motion of the bullet.
The work done by a force can be calculated using the formula:
Work = Force × Distance × cos(θ)
Where:
- Force is the magnitude of the resistive force acting on the bullet.
- Distance is the distance over which the resistive force is acting.
- θ is the angle between the direction of the force and displacement.
In this case, the resistive force acts opposite to the direction of the bullet's velocity, so the angle between the force and displacement is 180°. The cosine of 180° is -1. Therefore, the formula can be simplified to:
Work = - Force × Distance
Now, let's calculate the work done by the resistive force. We know the bullet's mass (30g) and velocity (200 m/s), so we can calculate its initial kinetic energy using the formula:
Kinetic Energy = 0.5 × mass × (velocity)^2
Plugging in the values, we have:
Kinetic Energy = 0.5 × 0.03 kg × (200 m/s)^2
= 0.5 × 0.03 kg × 40000 m^2/s^2
= 600 J
Since no external forces act on the bullet, the work done by the resistive force is equal to the decrease in kinetic energy. In this case, the bullet comes to rest, so its final kinetic energy is zero. Therefore, the work done by the resistive force is:
Work = Final Kinetic Energy - Initial Kinetic Energy
= 0 - 600 J
= -600 J
Since work is equal to the force multiplied by the distance, we can rearrange the equation to solve for the average resistive force:
Force = Work / Distance
Plugging in the values, we have:
Force = -600 J / 0.12 m
= -5000 N
The negative sign indicates that the force acts in the opposite direction of the displacement. Therefore, the average resistive force acting on the bullet is 5000 N.