Question

How much momentum will a dummbell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 ms-2

Answer 1

Answer:

Known Terms:-

u = Initial speed

v = Final speed

a = Acceleration

m = Mass

s = Distance.

Given:-

Mass of the dummbell, m = 10 kg

Distance attain by the dummbell, s = 80 cm = 0.8 m

Acceleration in the downward direction, a = 10 m/s²

Initial velocity of the dummbell, u = 0 (Because dummbell starts from rest.)

To Calculate:-

1. Final velocity of the dummbell (v)

2. Momentum of dummbell.

Formula to be used:-

v² = u² + 2 as

p = m v

Solution:-

Putting all the values, we get

v² = u² + 2 as

v² = 0 + 2 (10) 0.8

v² = 16

v = 4 m/s

Momentum, p = m v

= 10×4

= 40 kg m/s

Hence, the momentum with which the dummbell hits the floor is 40 kg m/s.

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Dummbell mass is 10 kg

Dummbell distance is 80 cm

As per situation covert it into metre

Acceleration = 80 cm

Acceleration = 0.8 m

Downward acceleration is 10 m/s^2

Dummbell initial velocity is 0 (Reason = It start from rest position as given in Question)

Using third equation of Motion

v² = u² + 2as

Substitute the values in Equation we get :-

v² = 0 + 2 (10) × 0.8

v² = 16

$v = \sqrt{16}$

v = 4 m/s

Momentum = m × v

= 10 × 4

= 40 kg m/s

Momentum is 40 kg m/s.