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Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it. When the spring is released, the balls nove with a velocity of 10 ms^-1. Find the acceleration produced in each ball if the spring constant is 4 N m^-1 ?
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Given:
- Mass of each ball = 2 kg
- Velocity of the balls = 10 m/s
- Spring constant = 4 N/m
Acceleration produced in each ball:
To find the acceleration produced in each ball, we can use the equation of motion:
Force = mass × acceleration
The force acting on each ball is provided by the compressed spring. According to Hooke's Law, the force exerted by a spring is directly proportional to its displacement from the equilibrium position. The equation for the force exerted by a spring is given by:
Force = spring constant × displacement
Hence, the force exerted by the spring on each ball can be calculated as:
Force = 4 N/m × displacement
Since the balls are initially at rest, the displacement of the spring is equal to the initial compression of the spring. Let's assume this initial compression as 'x'.
Force = 4 N/m × x
Using Newton's second law of motion, the equation becomes:
mass × acceleration = 4 N/m × x
Since both balls have the same mass and acceleration, we can rewrite the equation as:
2 kg × acceleration = 4 N/m × x
Simplifying the equation, we get:
acceleration = (4 N/m × x) / 2 kg
Given that the velocity of the balls after the spring is released is 10 m/s, we can use the equation of motion to relate the displacement and velocity:
velocity^2 = initial velocity^2 + 2 × acceleration × displacement
Since the initial velocity is zero, the equation becomes:
velocity^2 = 2 × acceleration × displacement
Plugging in the values, we have:
(10 m/s)^2 = 2 × acceleration × x
Simplifying the equation, we get:
acceleration = (10 m/s)^2 / (2 × x)
Equating the two expressions for acceleration, we have:
(4 N/m × x) / 2 kg = (10 m/s)^2 / (2 × x)
Simplifying the equation further, we get:
2 N/m × x^2 = 100 m^2/s^2
Solving for x, we find:
x^2 = 100 m^2/s^2 / 2 N/m
x^2 = 50 m
Taking the square root of both sides, we get:
x = √50 m
Hence, the displacement of the spring is equal to √50 m.
Substituting this value back into the equation for acceleration, we can find the acceleration produced in each ball:
acceleration = (4 N/m × √50 m) / 2 kg
Simplifying the equation, we find:
acceleration ≈ 4 ms^-2
Therefore, the acceleration produced in each ball is approximately 4 m/s².
- Mass of each ball = 2 kg
- Velocity of the balls = 10 m/s
- Spring constant = 4 N/m
Acceleration produced in each ball:
To find the acceleration produced in each ball, we can use the equation of motion:
Force = mass × acceleration
The force acting on each ball is provided by the compressed spring. According to Hooke's Law, the force exerted by a spring is directly proportional to its displacement from the equilibrium position. The equation for the force exerted by a spring is given by:
Force = spring constant × displacement
Hence, the force exerted by the spring on each ball can be calculated as:
Force = 4 N/m × displacement
Since the balls are initially at rest, the displacement of the spring is equal to the initial compression of the spring. Let's assume this initial compression as 'x'.
Force = 4 N/m × x
Using Newton's second law of motion, the equation becomes:
mass × acceleration = 4 N/m × x
Since both balls have the same mass and acceleration, we can rewrite the equation as:
2 kg × acceleration = 4 N/m × x
Simplifying the equation, we get:
acceleration = (4 N/m × x) / 2 kg
Given that the velocity of the balls after the spring is released is 10 m/s, we can use the equation of motion to relate the displacement and velocity:
velocity^2 = initial velocity^2 + 2 × acceleration × displacement
Since the initial velocity is zero, the equation becomes:
velocity^2 = 2 × acceleration × displacement
Plugging in the values, we have:
(10 m/s)^2 = 2 × acceleration × x
Simplifying the equation, we get:
acceleration = (10 m/s)^2 / (2 × x)
Equating the two expressions for acceleration, we have:
(4 N/m × x) / 2 kg = (10 m/s)^2 / (2 × x)
Simplifying the equation further, we get:
2 N/m × x^2 = 100 m^2/s^2
Solving for x, we find:
x^2 = 100 m^2/s^2 / 2 N/m
x^2 = 50 m
Taking the square root of both sides, we get:
x = √50 m
Hence, the displacement of the spring is equal to √50 m.
Substituting this value back into the equation for acceleration, we can find the acceleration produced in each ball:
acceleration = (4 N/m × √50 m) / 2 kg
Simplifying the equation, we find:
acceleration ≈ 4 ms^-2
Therefore, the acceleration produced in each ball is approximately 4 m/s².
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Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it. When the spring is released, the balls nove with a velocity of 10 ms^-1. Find the acceleration produced in each ball if the spring constant is 4 N m^-1 ?
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Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it. When the spring is released, the balls nove with a velocity of 10 ms^-1. Find the acceleration produced in each ball if the spring constant is 4 N m^-1 ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it. When the spring is released, the balls nove with a velocity of 10 ms^-1. Find the acceleration produced in each ball if the spring constant is 4 N m^-1 ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it. When the spring is released, the balls nove with a velocity of 10 ms^-1. Find the acceleration produced in each ball if the spring constant is 4 N m^-1 ?.
Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it. When the spring is released, the balls nove with a velocity of 10 ms^-1. Find the acceleration produced in each ball if the spring constant is 4 N m^-1 ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it. When the spring is released, the balls nove with a velocity of 10 ms^-1. Find the acceleration produced in each ball if the spring constant is 4 N m^-1 ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it. When the spring is released, the balls nove with a velocity of 10 ms^-1. Find the acceleration produced in each ball if the spring constant is 4 N m^-1 ?.
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