A bullet of mass 0.04 kg moving with a speed of 6 m per second enters ...
First, we have to find it's acceleration
v^2 = u^2 + 2 as
v = 0; u = 90 m/s ; s = 0.6 m (60 cm)
0 = (90)^2 + 2 x a x0.6
0 = 8100 + 1.2 a
-8100 = 1.2 a
a = - 8100/1.2 = -6750 m/s^2
average resistive force exerted by the block on bullet =?
= mass x acceleration
= 0.04 kg x -6750 m/s^2
= 270 N (avg. only)
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A bullet of mass 0.04 kg moving with a speed of 6 m per second enters ...
Given:
- Mass of the bullet (m) = 0.04 kg
- Initial velocity of the bullet (u) = 6 m/s
- Distance traveled by the bullet inside the block (s) = 60 cm = 0.6 m
To find:
- Average resistive force exerted by the block on the bullet
Formula:
The work done by a force is given by the formula: W = F * d * cos(θ)
where,
W is the work done,
F is the force applied,
d is the displacement,
θ is the angle between the force and the displacement.
Here, the force applied by the block on the bullet is in the opposite direction of the bullet's motion, so θ = 180 degrees. Therefore, cos(180) = -1.
The work done by the resistive force is equal to the change in kinetic energy of the bullet.
Step 1: Calculate the final velocity of the bullet (v).
Using the equation, v^2 = u^2 + 2as, where a is the acceleration and is equal to 0 because the bullet is stopped, we can find v.
v^2 = u^2 + 2as
v^2 = 6^2 + 2(0)(0.6)
v^2 = 36
v = √36
v = 6 m/s
Step 2: Calculate the change in kinetic energy (ΔKE).
The change in kinetic energy is given by the formula: ΔKE = (1/2)mv^2 - (1/2)mu^2
ΔKE = (1/2)(0.04)(6^2) - (1/2)(0.04)(6^2)
ΔKE = (1/2)(0.04)(36 - 36)
ΔKE = 0
Step 3: Calculate the work done by the resistive force (W).
The work done by the resistive force is equal to the change in kinetic energy of the bullet.
W = -ΔKE
W = -0
W = 0
Step 4: Calculate the average resistive force (F).
The average resistive force exerted by the block on the bullet is equal to the work done divided by the distance traveled by the bullet inside the block.
F = W / d
F = 0 / 0.6
F = 0 N
Explanation:
The average resistive force exerted by the block on the bullet is 0 N. This means that the block exerted no resistive force on the bullet as it traveled through it. Since the bullet came to a stop, the work done by the resistive force is zero. The change in kinetic energy of the bullet is also zero, indicating that there was no change in the bullet's energy. Therefore, the average resistive force exerted by the block on the bullet is zero.
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