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A block Of mass 1 kg falls freely on a spring from a height Of 20 CM as shown in find the compression in the spring if it's force constant is 10>3n/m?
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**Solution:**

When a block of mass 1 kg falls freely from a height of 20 cm on a spring, the potential energy of the block is converted into the spring potential energy.

We can use the principle of conservation of energy to find the maximum compression in the spring. According to this principle, the total energy of a closed system remains constant.

The total energy of the system is given by:

Total energy = Potential energy + Kinetic energy + Spring potential energy

Initially, the block has only potential energy, given by:

Potential energy = mgh

where m is the mass of the block, g is the acceleration due to gravity, and h is the height from which the block is dropped.

Potential energy = 1 x 9.8 x 0.2 = 1.96 J

As the block falls, its potential energy is converted into kinetic energy, given by:

Kinetic energy = (1/2)mv^2

where m is the mass of the block and v is its velocity just before it hits the spring.

The velocity of the block just before it hits the spring can be found from the conservation of energy equation:

Total energy = Potential energy + Kinetic energy + Spring potential energy

At the maximum compression of the spring, the kinetic energy of the block is zero. Therefore, the total energy of the system is equal to the sum of its potential energy and spring potential energy.

Total energy = Potential energy + Spring potential energy

The spring potential energy is given by:

Spring potential energy = (1/2)kx^2

where k is the force constant of the spring and x is the compression in the spring.

Substituting the values of potential energy, spring potential energy, and force constant, we get:

1.96 J = (1/2)kx^2

x^2 = (2 x 1.96) / k

x^2 = 0.00392

x = 0.0626 m

Therefore, the maximum compression in the spring is 6.26 cm.

**Explanation:**

The solution is based on the principle of conservation of energy. The potential energy of the block is converted into kinetic energy just before it hits the spring. At the maximum compression of the spring, the kinetic energy is zero, and all the energy is stored in the spring potential energy. This spring potential energy is given by (1/2)kx^2, where k is the force constant of the spring and x is the compression in the spring. By equating the total energy of the system to the sum of its potential and spring potential energy, we can find the maximum compression in the spring.
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A block Of mass 1 kg falls freely on a spring from a height Of 20 CM as shown in find the compression in the spring if it's force constant is 10>3n/m?
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A block Of mass 1 kg falls freely on a spring from a height Of 20 CM as shown in find the compression in the spring if it's force constant is 10>3n/m? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A block Of mass 1 kg falls freely on a spring from a height Of 20 CM as shown in find the compression in the spring if it's force constant is 10>3n/m? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block Of mass 1 kg falls freely on a spring from a height Of 20 CM as shown in find the compression in the spring if it's force constant is 10>3n/m?.
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