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From a rifle of mass 4kg a bullet of mass 50g is fired with initial velocity of 35m/s. calculate the initial recoil velocity of the rifle?
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From a rifle of mass 4kg a bullet of mass 50g is fired with initial ve...
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Mass of the rifle, m1= 4 kg
Mass of the bullet, m2= 50g= 0.05 kg
Recoil velocity of the rifle= v1
Bullet is fired with an initial velocity, v2= 35m/s
Initially, the rifle is at rest.
Thus, its initial velocity, v= 0
Total initial momentum of the rifle and bullet system= (m1+m2)v= 0
Total momentum of the rifle and bullet system after firing:
= m1v1 + m2v2= 0.05 — 35= 4v1 + 1.75
According to the law of conservation of momentum:
Total momentum after the firing = Total momentum before the firing 4v1 + 1.75= 0
v1= -1.75 / 4= -0.4375 m/s
The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 m/s.
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From a rifle of mass 4kg a bullet of mass 50g is fired with initial ve...
Calculation of the Initial Recoil Velocity of the Rifle
To calculate the initial recoil velocity of the rifle, we can use the law of conservation of momentum. According to this law, the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can use the formula:
Momentum = mass × velocity
Given:
Mass of the rifle (m1) = 4 kg
Mass of the bullet (m2) = 50 g = 0.05 kg
Initial velocity of the bullet (v2) = 35 m/s
Step 1: Converting units
The mass of the bullet is given in grams, but we need to convert it to kilograms to maintain consistency. Therefore, the mass of the bullet is 0.05 kg.
Step 2: Calculating the momentum of the bullet
Momentum of the bullet (p2) = m2 × v2
= 0.05 kg × 35 m/s
= 1.75 kg·m/s
Step 3: Applying the law of conservation of momentum
According to the law of conservation of momentum, the total momentum before the event (bullet fired) is equal to the total momentum after the event (recoil of the rifle).
Initial momentum of the system (before firing) = Final momentum of the system (after firing)
Let the initial velocity of the rifle be v1.
Initial momentum of the system (before firing) = (m1 + m2) × v1
Final momentum of the system (after firing) = (m1 × v1) + (m2 × v2)
Therefore, (m1 + m2) × v1 = (m1 × v1) + (m2 × v2)
Step 4: Solving for the initial recoil velocity of the rifle
Rearranging the equation, we get:
(m1 + m2) × v1 = (m1 × v1) + (m2 × v2)
Expanding the equation, we have:
m1 × v1 + m2 × v1 = m1 × v1 + m2 × v2
Subtracting (m1 × v1) from both sides, we get:
m2 × v1 = m2 × v2
Dividing both sides by m2, we have:
v1 = v2
Therefore, the initial recoil velocity of the rifle is equal to the initial velocity of the bullet, which is 35 m/s.
To calculate the initial recoil velocity of the rifle, we can use the law of conservation of momentum. According to this law, the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can use the formula:
Momentum = mass × velocity
Given:
Mass of the rifle (m1) = 4 kg
Mass of the bullet (m2) = 50 g = 0.05 kg
Initial velocity of the bullet (v2) = 35 m/s
Step 1: Converting units
The mass of the bullet is given in grams, but we need to convert it to kilograms to maintain consistency. Therefore, the mass of the bullet is 0.05 kg.
Step 2: Calculating the momentum of the bullet
Momentum of the bullet (p2) = m2 × v2
= 0.05 kg × 35 m/s
= 1.75 kg·m/s
Step 3: Applying the law of conservation of momentum
According to the law of conservation of momentum, the total momentum before the event (bullet fired) is equal to the total momentum after the event (recoil of the rifle).
Initial momentum of the system (before firing) = Final momentum of the system (after firing)
Let the initial velocity of the rifle be v1.
Initial momentum of the system (before firing) = (m1 + m2) × v1
Final momentum of the system (after firing) = (m1 × v1) + (m2 × v2)
Therefore, (m1 + m2) × v1 = (m1 × v1) + (m2 × v2)
Step 4: Solving for the initial recoil velocity of the rifle
Rearranging the equation, we get:
(m1 + m2) × v1 = (m1 × v1) + (m2 × v2)
Expanding the equation, we have:
m1 × v1 + m2 × v1 = m1 × v1 + m2 × v2
Subtracting (m1 × v1) from both sides, we get:
m2 × v1 = m2 × v2
Dividing both sides by m2, we have:
v1 = v2
Therefore, the initial recoil velocity of the rifle is equal to the initial velocity of the bullet, which is 35 m/s.
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From a rifle of mass 4kg a bullet of mass 50g is fired with initial velocity of 35m/s. calculate the initial recoil velocity of the rifle?
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From a rifle of mass 4kg a bullet of mass 50g is fired with initial velocity of 35m/s. calculate the initial recoil velocity of the rifle? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about From a rifle of mass 4kg a bullet of mass 50g is fired with initial velocity of 35m/s. calculate the initial recoil velocity of the rifle? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a rifle of mass 4kg a bullet of mass 50g is fired with initial velocity of 35m/s. calculate the initial recoil velocity of the rifle?.
From a rifle of mass 4kg a bullet of mass 50g is fired with initial velocity of 35m/s. calculate the initial recoil velocity of the rifle? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about From a rifle of mass 4kg a bullet of mass 50g is fired with initial velocity of 35m/s. calculate the initial recoil velocity of the rifle? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a rifle of mass 4kg a bullet of mass 50g is fired with initial velocity of 35m/s. calculate the initial recoil velocity of the rifle?.
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