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A car of mass M travelling with speed V collides with a spring having spring constant K the car comes to rest when spring is compressed to a distance of Xm find Xm?
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A car of mass M travelling with speed V collides with a spring having ...
Introduction:
When a car collides with a spring, the kinetic energy of the car is transferred to the spring, causing it to compress. The car comes to rest when the spring has compressed to a certain distance. In this scenario, we need to find the compression distance Xm of the spring.
Given:
- Mass of the car (M)
- Speed of the car before collision (V)
- Spring constant (K)
Explanation:
Step 1: Determine the initial kinetic energy of the car
The initial kinetic energy (KE) of the car can be calculated using the formula:
KE = 0.5 * M * V^2
Step 2: Determine the potential energy of the compressed spring
The potential energy (PE) of the compressed spring can be calculated using the formula:
PE = 0.5 * K * Xm^2
Step 3: Equate the initial kinetic energy with the potential energy of the spring
Since the energy is conserved in this collision, we can equate the initial kinetic energy with the potential energy of the spring:
0.5 * M * V^2 = 0.5 * K * Xm^2
Step 4: Solve for Xm
To find Xm, we rearrange the equation and solve for Xm:
Xm = sqrt((M * V^2) / K)
Conclusion:
The compression distance of the spring (Xm) can be determined using the equation:
Xm = sqrt((M * V^2) / K)
This equation allows us to calculate the compression distance of the spring when a car of mass M collides with it at a speed of V, given the spring constant K.
When a car collides with a spring, the kinetic energy of the car is transferred to the spring, causing it to compress. The car comes to rest when the spring has compressed to a certain distance. In this scenario, we need to find the compression distance Xm of the spring.
Given:
- Mass of the car (M)
- Speed of the car before collision (V)
- Spring constant (K)
Explanation:
Step 1: Determine the initial kinetic energy of the car
The initial kinetic energy (KE) of the car can be calculated using the formula:
KE = 0.5 * M * V^2
Step 2: Determine the potential energy of the compressed spring
The potential energy (PE) of the compressed spring can be calculated using the formula:
PE = 0.5 * K * Xm^2
Step 3: Equate the initial kinetic energy with the potential energy of the spring
Since the energy is conserved in this collision, we can equate the initial kinetic energy with the potential energy of the spring:
0.5 * M * V^2 = 0.5 * K * Xm^2
Step 4: Solve for Xm
To find Xm, we rearrange the equation and solve for Xm:
Xm = sqrt((M * V^2) / K)
Conclusion:
The compression distance of the spring (Xm) can be determined using the equation:
Xm = sqrt((M * V^2) / K)
This equation allows us to calculate the compression distance of the spring when a car of mass M collides with it at a speed of V, given the spring constant K.
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A car of mass M travelling with speed V collides with a spring having spring constant K the car comes to rest when spring is compressed to a distance of Xm find Xm?
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A car of mass M travelling with speed V collides with a spring having spring constant K the car comes to rest when spring is compressed to a distance of Xm find Xm? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A car of mass M travelling with speed V collides with a spring having spring constant K the car comes to rest when spring is compressed to a distance of Xm find Xm? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car of mass M travelling with speed V collides with a spring having spring constant K the car comes to rest when spring is compressed to a distance of Xm find Xm?.
A car of mass M travelling with speed V collides with a spring having spring constant K the car comes to rest when spring is compressed to a distance of Xm find Xm? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A car of mass M travelling with speed V collides with a spring having spring constant K the car comes to rest when spring is compressed to a distance of Xm find Xm? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car of mass M travelling with speed V collides with a spring having spring constant K the car comes to rest when spring is compressed to a distance of Xm find Xm?.
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