Question

58. A mass of 0.5 kg moving with a speed of 1.5 m/s
on a horizontal smooth surface, collides with a
nearly weightless spring of force constant
k=50N/m. The maximum compression of the
spring would be :-​

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

• Mass of the body (m) = 0.5 Kg.
• Spring constant (K) = 50 N/m.
• Speed of the body (v) = 1.5 m/s.
• Let the compression of the spring be "x".

$\huge{\bold{\underline{Explanation:-}}}$

$\rule{300}{1.5}$

According to law of conservation of energy,

Kinetic energy of the body = Potential energy of the spring.

Now,

$\large{\tt K.E = U}$

Substituting the formula,

$\large{\tt \dfrac{1}{2} mv^2 = \dfrac{1}{2}Kx^2}$

Substituting the values,

$\large{\tt \dfrac{1}{2} 0.5 \times (1.5)^2 = \dfrac{1}{2} \times 50 \times x^2}$

½ gets cancel on both sides,

$\large{\tt \cancel{\dfrac{1}{2}} 0.5 \times (1.5)^2 = \cancel{\dfrac{1}{2}} \times 50 \times x^2}$

$\large{\tt 0.5 \times 1.5 \times 1.5 = 50 \times x^2}$

$\large{\tt 0.5 \times 2.25 = 50 \times x^2}$

$\large{\tt x^2 = \dfrac{0.5 \times 2.25}{50}}$

$\large{\tt x^2 = \dfrac{\cancel{0.5} \times 2.25}{\cancel{50}}}$

$\large{\tt x^2 = 0.01 \times 2.25}$

$\large{\tt x^2 = \dfrac{1}{100} \times \dfrac{225}{100}}$

$\large{\tt x = \sqrt{\dfrac{1}{100} \times \dfrac{225}{100}}}$

$\large{\tt x = \dfrac{1}{10} \times \dfrac{15}{10}}$

$\large{\tt x = \dfrac{15}{100}}$

$\huge{\boxed{\boxed{\tt x = 0.15 \: meters}}}$

So, the maximum compression of the spring will be 0.15 meters.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Law of conservation of energy:-

It states that Energy cannot be created nor destroyed in a process.But it can be transformed from one form to other forms.

Example:-

• During a free fall the body's energy changes from potential energy to Kinetic energy.
• In dams the Energy stored in water (Potential energy) Is converted to Electrical energy.

$\rule{300}{1.5}$

Answer 2

Mass of the body (m) = 0.5 Kg.

Spring constant (K) = 50 N/m.

Speed of the body (v) = 1.5 m/s.

Let the compression of the spring be "x".

According to law of conservation of energy,

Kinetic energy of the body = Potential energy of the spring.

Now,

Substituting the formula,

Substituting the values,

½ gets cancel on both sides,

So, the maximum compression of the spring will be 0.15 meters.

Law of conservation of energy:-

It states that Energy cannot be created nor destroyed in a process.But it can be transformed from one form to other forms.

Example:-

During a free fall the body's energy changes from potential energy to Kinetic energy.

In dams the Energy stored in water (Potential energy) Is converted to Electrical energy.