A cannon on a stationery railway truck fires a shell of mass 5 kg with a velocity of 240 m.s -1. The mass of the cannon is 600kg. The cannon recoils and moves back on the rails and collides with a stationery truck of mass 400 kg. The velocity of the cannon after the collision is 0.8 m.s -1. With what velocity does the second truck move after the collision.
To answer this question, we can use the principle of conservation of momentum. According to this principle, the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.
Let's denote the initial velocity of the cannon as v1, the final velocity of the cannon as vf1, and the final velocity of the second truck as vf2.
Step 1: Find the initial momentum of the system.
The initial momentum of the system is given by the sum of the momentum of the cannon and the momentum of the shell.
Initial momentum = (mass of the cannon x initial velocity of the cannon) + (mass of the shell x initial velocity of the shell)
Initial momentum = (600 kg x v1) + (5 kg x 240 m/s)
Step 2: Find the final momentum of the system.
The final momentum of the system is given by the sum of the momentum of the cannon and the momentum of the second truck.
Final momentum = (mass of the cannon x final velocity of the cannon) + (mass of the second truck x final velocity of the second truck)
Final momentum = (600 kg x vf1) + (400 kg x vf2)
Step 3: Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the initial momentum should be equal to the final momentum.
(600 kg x v1) + (5 kg x 240 m/s) = (600 kg x vf1) + (400 kg x vf2)
Step 4: Use the given information to solve the equation.
We know that the final velocity of the cannon after the collision is 0.8 m/s, so vf1 = 0.8 m/s.
The equation becomes: (600 kg x v1) + (5 kg x 240 m/s) = (600 kg x 0.8 m/s) + (400 kg x vf2)
Step 5: Solve the equation to find the value of vf2.
Rearranging the equation, we have:
(600 kg x v1) + (5 kg x 240 m/s) - (600 kg x 0.8 m/s) = 400 kg x vf2
(600 kg x v1) + (5 kg x 240 m/s) - (600 kg x 0.8 m/s) = 400 kg x vf2
(600 kg x v1) + (5 kg x 240 m/s) - (480 kg m/s) = 400 kg x vf2
(600 kg x v1) - (480 kg m/s) = 400 kg x vf2 - (5 kg x 240 m/s)
Now, you need to substitute the given values of the cannon's mass, shell's mass, initial velocity of the shell, final velocity of the cannon, and solve the equation to find the value of vf2.
To solve this problem, we can apply the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.
Let's break down the problem step by step:
Step 1: Calculate the initial momentum of the cannon and the shell together before the collision.
The initial momentum (p) is given by the equation:
p = m*v
where m is the mass and v is the velocity.
The initial momentum (P_initial) of the cannon and shell is:
P_initial = (mass of cannon + mass of shell) * velocity of cannon and shell
Given:
Mass of cannon (m1) = 600 kg
Mass of shell (m2) = 5 kg
Velocity of cannon and shell (v1) = 240 m/s
P_initial = (m1 + m2) * v1
P_initial = (600 kg + 5 kg) * 240 m/s
P_initial = 605 kg * 240 m/s
Step 2: Calculate the final momentum of the cannon and the shell together after the collision.
The final momentum (P_final) is given by the equation:
P_final = (mass of cannon + mass of shell) * velocity of cannon and shell after the collision
Given:
Velocity of cannon and shell after the collision (v2) = 0.8 m/s
P_final = (m1 + m2) * v2
P_final = (600 kg + 5 kg) * 0.8 m/s
P_final = 605 kg * 0.8 m/s
Step 3: Apply the conservation of momentum principle.
According to the principle of conservation of momentum, the initial momentum (P_initial) must be equal to the final momentum (P_final).
P_initial = P_final
605 kg * 240 m/s = 605 kg * 0.8 m/s
Step 4: Solve for the velocity of the second truck.
To find the velocity of the second truck (v3), we need to rearrange the equation:
v3 = (605 kg * 240 m/s) / 400 kg
v3 = 144600 kg·m/s / 400 kg
v3 = 361.5 m/s
Therefore, the second truck will move with a velocity of 361.5 m/s after the collision.