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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
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- 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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To solve this problem, we can start by considering the forces acting on the block when it slides on the horizontal floor:
1. Weight (mg): The weight of the block is given by the mass (m) multiplied by the acceleration due to gravity (g), where g ≈ 9.8 m/s².
2. Normal force (N): The normal force exerted by the floor on the block is equal in magnitude and opposite in direction to the weight of the block.
3. Kinetic friction force (fk): The kinetic friction force opposes the motion of the block and is given by the coefficient of kinetic friction (μk) multiplied by the normal force.
From the given information, we know that the kinetic friction force is 15 N.
Next, let's consider the forces acting on the block when it strikes the uncompressed spring:
4. Spring force (Fs): The spring force is proportional to the displacement of the spring from its equilibrium position and is given by Hooke's Law: Fs = -kx, where k is the spring constant and x is the displacement of the spring.
Initially, when the block strikes the uncompressed spring, the only force acting on it is the kinetic friction force, which opposes its motion. As a result, the block will decelerate.
When the block comes to rest, the kinetic friction force is equal in magnitude and opposite in direction to the spring force. Therefore, we can equate these two forces:
fk = Fs
Substituting the given values, we have:
15 N = -kx
Given that the spring constant (k) is 10000 N/m, we can solve for the displacement of the spring (x):
x = -15 N / 10000 N/m
x = -0.0015 m
Since the displacement is negative, indicating compression, we can take the absolute value to find the magnitude of the compression:
x = 0.0015 m
Finally, converting the displacement to centimeters, we have:
x = 0.0015 m * 100 cm/m = 0.15 cm
Therefore, the spring compresses by 0.15 cm or 1.5 mm.
1. Weight (mg): The weight of the block is given by the mass (m) multiplied by the acceleration due to gravity (g), where g ≈ 9.8 m/s².
2. Normal force (N): The normal force exerted by the floor on the block is equal in magnitude and opposite in direction to the weight of the block.
3. Kinetic friction force (fk): The kinetic friction force opposes the motion of the block and is given by the coefficient of kinetic friction (μk) multiplied by the normal force.
From the given information, we know that the kinetic friction force is 15 N.
Next, let's consider the forces acting on the block when it strikes the uncompressed spring:
4. Spring force (Fs): The spring force is proportional to the displacement of the spring from its equilibrium position and is given by Hooke's Law: Fs = -kx, where k is the spring constant and x is the displacement of the spring.
Initially, when the block strikes the uncompressed spring, the only force acting on it is the kinetic friction force, which opposes its motion. As a result, the block will decelerate.
When the block comes to rest, the kinetic friction force is equal in magnitude and opposite in direction to the spring force. Therefore, we can equate these two forces:
fk = Fs
Substituting the given values, we have:
15 N = -kx
Given that the spring constant (k) is 10000 N/m, we can solve for the displacement of the spring (x):
x = -15 N / 10000 N/m
x = -0.0015 m
Since the displacement is negative, indicating compression, we can take the absolute value to find the magnitude of the compression:
x = 0.0015 m
Finally, converting the displacement to centimeters, we have:
x = 0.0015 m * 100 cm/m = 0.15 cm
Therefore, the spring compresses by 0.15 cm or 1.5 mm.
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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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