Question

A mass of 10 kg is dropped from a height of 50cm. Find its a) kinetic enetgy b) velocity just as it reaches the ground. Does the velocity depends on the mass of the particle? Explain (acceletation g=10m/s)

Answer 1

Explanation:

Mass=10 kg

Height=50cm-0.5m

So W=m*g*h

=10*10*0.5

= 50 Joules

Answer 2

So we have,

m = 10 kg ; h = 50 cm ; u = 0 m s^(-1) ; a = g = 10 m s^(-1)

Now, by the equation,

v² = u² + 2as

by replacing 's' by 'h',

v² = 2 · 10 · 50 = 1000

=> v = 10√10 m s^(-1)

Well, this should be the velocity just as it reaches the ground. So, kinetic energy,

K = (m v²) / 2

K = 10 · 1000 / 2

K = 5 kJ

Now we check whether the velocity of the body is dependent on its mass.

We have kinetic energy, K = (m v²) / 2.

If K is a constant, assuming m not being a constant, we have,

m = 2K / v²

This implies that m is inversely proportional to the second power of v, i.e., as m increases, v decreases by its second power. But this does not happen since the kinetic energy not being a constant.

So we can say that mass and velocity are not dependent to each other.

Or, we have the first equation of motion,

v = u + a t

Here u = 0 and a = g. So,

v = g t

This implies v is only dependent on g and t. But, by the universal law of gravitation, we have an expression for g, i.e.,

g = G M / R²,

where G is the gravitational constant, M and R being the mass and the radius of the earth respectively. So,

v = G M t / R²

This does not say that the velocity depends on the mass of the falling body.