Question

A block of mass 5 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block. The block is given a sharp impulse from below, so that it acquires an upward speed of 2⋅ m/s. How high will it rise? Take g = 10 m/s2.

Answer 1

The block of mass 5 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block  and it is given a sharp impulse from below , so that it acquires an upward speed of 2 m/s and it will rise up to  20 cm.

Explanation:

Step 1:

given data in the question  

Mass of the block = 5 kg.

Upward Speed, v = 2 m/sec.

Kinetic energy of the block =  m v² .

Step 2:

Assume the new block height will be h.

Therefore, at the highest point, the increase in potential energy is comparatively equal to Kinetic energy.

$m g h=\frac{1}{2} m v^{2}$

$h=\frac{1}{2 m g} m v^{2}$

$h=\frac{1}{2 m g} m v^{2}$

Cancel 'm' on both sides of the above equation

we get, $\mathrm{h}=\frac{1}{2 \mathrm{g}} \mathrm{v}^{2}$

Step 3:

g is called the gravity acceleration. The terrestrial value is $9.8 \frac{m}{s^{2}}$. In other words, the acceleration of gravity at sea level on the earth's surface is $9.8 \frac{m}{s^{2}} = 10 \frac{m}{s^{2}}$

$h=\frac{2^{2}}{2 \times 10}$

$h=\frac{4}{20}$

$h=\frac{2}{10}$

h= 0.2 meter

h = 20 centimeter

It will grow to 20 cm.

Answer 2

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