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A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by
[AIEEE 2007]
- a)5.5 cm
- b)2.5 cm
- c)11.0 cm
- d)8.5 cm
Correct answer is option 'A'. Can you explain this answer?
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Given:
- Mass of the block (m) = 2 kg
- Initial speed of the block (v) = 4 m/s
- Kinetic friction force (fk) = 15 N
- Spring constant (k) = 10000 N/m
To find:
- Compression of the spring (x)
Assumptions:
- The surface is horizontal.
- The block and spring are the only objects involved in the motion.
- There is no loss of energy due to other factors like air resistance.
Solution:
1. Initial Kinetic Energy:
- The initial kinetic energy of the block is given by the formula:
KE_initial = 0.5 * m * v^2
= 0.5 * 2 * (4)^2
= 16 J
2. Work Done by Friction:
- The work done by friction force is given by:
Work_friction = fk * d
= 15 * d (where d is the distance traveled by the block)
The block stops when the work done by friction is equal to the initial kinetic energy:
15 * d = 16
d = 16/15
d = 1.0667 m (approximately)
3. Work Done on the Spring:
- The work done on the spring is equal to the initial kinetic energy:
Work_spring = 16 J
4. Potential Energy of the Spring:
- The potential energy stored in the spring is given by the formula:
PE_spring = 0.5 * k * x^2 (where x is the compression of the spring)
We can equate the work done on the spring to the potential energy stored:
16 = 0.5 * 10000 * x^2
16 = 5000 * x^2
x^2 = 16/5000
x^2 = 0.0032
x = √0.0032
x ≈ 0.0566 m (approximately)
5. Conversion to Centimeters:
- The compression of the spring in centimeters is given by:
x_cm = x * 100
= 0.0566 * 100
= 5.66 cm (approximately)
Therefore, the spring compresses by approximately 5.66 cm. Hence, the correct answer is option 'A' (5.5 cm).
- Mass of the block (m) = 2 kg
- Initial speed of the block (v) = 4 m/s
- Kinetic friction force (fk) = 15 N
- Spring constant (k) = 10000 N/m
To find:
- Compression of the spring (x)
Assumptions:
- The surface is horizontal.
- The block and spring are the only objects involved in the motion.
- There is no loss of energy due to other factors like air resistance.
Solution:
1. Initial Kinetic Energy:
- The initial kinetic energy of the block is given by the formula:
KE_initial = 0.5 * m * v^2
= 0.5 * 2 * (4)^2
= 16 J
2. Work Done by Friction:
- The work done by friction force is given by:
Work_friction = fk * d
= 15 * d (where d is the distance traveled by the block)
The block stops when the work done by friction is equal to the initial kinetic energy:
15 * d = 16
d = 16/15
d = 1.0667 m (approximately)
3. Work Done on the Spring:
- The work done on the spring is equal to the initial kinetic energy:
Work_spring = 16 J
4. Potential Energy of the Spring:
- The potential energy stored in the spring is given by the formula:
PE_spring = 0.5 * k * x^2 (where x is the compression of the spring)
We can equate the work done on the spring to the potential energy stored:
16 = 0.5 * 10000 * x^2
16 = 5000 * x^2
x^2 = 16/5000
x^2 = 0.0032
x = √0.0032
x ≈ 0.0566 m (approximately)
5. Conversion to Centimeters:
- The compression of the spring in centimeters is given by:
x_cm = x * 100
= 0.0566 * 100
= 5.66 cm (approximately)
Therefore, the spring compresses by approximately 5.66 cm. Hence, the correct answer is option 'A' (5.5 cm).
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A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by[AIEEE 2007]a)5.5 cmb)2.5 cmc)11.0 cmd)8.5 cmCorrect answer is option 'A'. Can you explain this answer?
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A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by[AIEEE 2007]a)5.5 cmb)2.5 cmc)11.0 cmd)8.5 cmCorrect answer is option 'A'. Can you explain this answer? 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 A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by[AIEEE 2007]a)5.5 cmb)2.5 cmc)11.0 cmd)8.5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by[AIEEE 2007]a)5.5 cmb)2.5 cmc)11.0 cmd)8.5 cmCorrect answer is option 'A'. Can you explain this answer?.
A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by[AIEEE 2007]a)5.5 cmb)2.5 cmc)11.0 cmd)8.5 cmCorrect answer is option 'A'. Can you explain this answer? 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 A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by[AIEEE 2007]a)5.5 cmb)2.5 cmc)11.0 cmd)8.5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by[AIEEE 2007]a)5.5 cmb)2.5 cmc)11.0 cmd)8.5 cmCorrect answer is option 'A'. Can you explain this answer?.
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