Question

Two spheres of mass 10 g and 100 g each falls on the two pans of a table balance from a height of 40 cm and 10 cm, respectively. If both are brought to rest in 0.1 second, determine the force exerted by each sphere on the pans.​

Answer 1

Given:

Two spheres of mass 10 g and 100 g each falls on the two pans of a table balance from a height of 40 cm and 10 cm, respectively. Both are brought to rest in 0.1 second.

To find:

Force exerted by each sphere on the pan.

Calculation:

For the 10 g pan:

Velocity just before hitting the pan:

$= > {v}^{2} = {u}^{2} + 2gh \\ = > {v}^{2} = 0 + (2 \times 10 \times 0.4) \\ = > {v}^{2} = 8 \\ = > v = 2 \sqrt{2} \: m {s}^{ - 1}$

Let force exerted be f:

$f = mass \times acc.$

$= > f = \dfrac{10}{1000} \times \dfrac{0 - 2 \sqrt{2} }{0.1} \\ = > f = 0.1 \times ( - 2 \sqrt{2} ) \\ \boxed{ = > f = - 0.2 \sqrt{2} \: N }$

For the 100 g mass:

Velocity just before hitting the pan:

$= > {v}^{2} = {u}^{2} + 2gh \\ = > {v}^{2} = 0 + (2 \times 10 \times 0.1) \\ = > {v}^{2} = 2 \\ = > v = \sqrt{2} \: m {s}^{ - 1}$

Let force be f:

$= > f = \dfrac{100}{1000} \times \dfrac{0 - \sqrt{2} }{0.1} \\ = > f = ( - \sqrt{2} ) \\ \boxed{= > f = - \sqrt{2} \: N }$