Question

How much linear momentum will be transferred by
a stone of mass 50 kg to the floor, if it falls from
height of 10 m? (Take downward acceleration to be
10 m/s)​

Answer 1

Answer:

pls see the attachment

Answer 2

The linear momentum transferred by the stone will be 707 Kg m/s

Given:

Mass of the stone = 50 Kg

Height = 10 m

Acceleration due to gravity = 10 m/s

To Find:

The linear momentum transferred by the stone

Solution:

The linear momentum can be calculated easily as given below.

A vector quantity called linear momentum is calculated by multiplying an object's mass, m, by its velocity, v.

Mathematically,

Linear momentum (p) = Mass (m) × Velocity (v)

p = m × v

We need to find the velocity of the stone.

We know that,

By equation of motion,

$s = ut + \frac{1}{2} at^{2}$

We have,

s = 10 m

u = 0 m/s

a = 10 m/s

t =?

By substituting the values,

$s = ut + \frac{1}{2} at^{2}$

10 = 0 + $\frac{1}{2}$ 10 × $t^{2}$

10 = 5 × $t^{2}$

Therefore,

$t^{2}$ = $\frac{10}{5}$

$t^{2}$ = 2

t = $\sqrt{2}$ s

We know that,

By equation of motion,

v = u + at

We have,

u = 0 m/s

a = 10 m/s

t = $\sqrt{2}$ s

By substituting the values,

v = u + at

v = 0 + 10 × $\sqrt{2$

v = 10 $\sqrt{2}$ m/s

Now,

We need to substitute the values of mass and velocity in the equation of momentum,

That is,

p = m × v

p = 50 × 10 $\sqrt{2}$

p = 500 $\sqrt{2}$

($\sqrt{2}$ = 1.414)

Therefore,

p = 500 × 1.414

p = 707 Kg m/s

Hence, the linear momentum transferred by the stone is 707 Kg m/s

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