A bullet of mass 100g moving with20m/sec .Strikes a wooden plank and peretrates up to 20cm.Calculate the resistance offered by the wooden plank.
To calculate the resistance offered by the wooden plank, we need to apply the principle of work and energy.
1. First, let's calculate the initial kinetic energy of the bullet using the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the bullet = 100 g = 0.1 kg
Velocity of the bullet = 20 m/s
Substituting the values:
Kinetic Energy = (1/2) * 0.1 * 20^2
= 40 J
2. Next, we need to calculate the work done by the resistance offered by the wooden plank using the formula:
Work = Force * Distance
The work done will be equal to the decrease in kinetic energy of the bullet.
Since the bullet comes to rest after penetrating the wooden plank, its kinetic energy is fully converted into workdone.
We can calculate the distance by converting the depth of penetration (20 cm = 0.2 m) to meters.
Distance = 0.2 m
Substituting the values:
Work = 40 J
3. Finally, we can calculate the resistance offered by the wooden plank using the formula:
Resistance = Work / Distance
Substituting the values:
Resistance = 40 J / 0.2 m
= 200 N
Hence, the resistance offered by the wooden plank is 200 Newtons (N).
To calculate the resistance offered by the wooden plank, we can use the principle of impulse and momentum.
The impulse, denoted by J, is equal to the change in momentum of the bullet. It can be calculated using the equation:
J = m * v
Where:
J = impulse
m = mass of the bullet
v = velocity of the bullet
Let's substitute the given values:
m = 100 g = 0.1 kg
v = 20 m/s
J = 0.1 kg * 20 m/s
J = 2 kg·m/s
Next, we'll calculate the average force, denoted by F, using the formula:
J = F * t
Where:
F = average force
t = time taken
The distance, denoted by d, can be calculated using the equation:
d = v * t
Where:
d = distance
v = velocity of the bullet
t = time taken
Rearranging the equation, we can solve for t:
t = d / v
Given that d = 0.2 m and v = 20 m/s:
t = 0.2 m / 20 m/s
t = 0.01 s
Now, substituting the values into the equation for average force:
2 kg·m/s = F * 0.01 s
Solving for F:
F = 2 kg·m/s / 0.01 s
F = 200 N
Therefore, the resistance offered by the wooden plank is 200 Newtons (N).
momentum = 0.100 * 20 = 2 kg m/s
distance into plank = .020 meter
average speed in plank = 20/2 = 10 m/s
time in plank = .020/10 = .002 s
average force = change in momentum/time
= 2/.002 = 1000 Newtons