Question

c) A body of mass 10 kg is kept at a height of 5 m. It is allowed to fall and reach the ground.
i) What is the total mechanical energy possessed by the body at a height of 2 m
assuming it is a frictionless medium.
ii) What is the kinetic energy possessed by the body just before hitting the ground? [g
10 m/s?].

Answer 1

Explanation :-

Given :

Mass,m = 10kg

Height,h = 5m

Velocity,v = 0 [as it was in rest]

Gravitational energy,g = 10m/s^2

To Find :

Total mechanical energy possessed by the body at a height of 2m assuming it is a frictionless medium = ?

Solution :

We know,

$\sf{}Mechanical\ energy=Kinetic\ energy+Potential\ energy$

So,

$\sf{}\implies Mechanical\ energy=\dfrac{1}{2}mv^2+mgh$

$\sf{}\implies Mechanical\ energy=\dfrac{1}{2}\times 5\times (0)^2+10\times 10\times 5$

$\sf{}\implies Mechanical\ energy=500J$

Total energy of the system remain conserve so the initial total energy will remain same.

Therefore,at a height of 2m body possess total energy of 500J

To Find :

Kinetic energy possessed by the bidy just before hitting the ground = ?

Given :

Mass,m = 10kg

Height,h = 5m

Initial velocity,u = 0

Gravitational energy,g = 10m/s^2

Solution :

ii) Kinetic energy possessed by the body just before hitting the ground is is 500J because it is about to reach the ground,potential energy will fully be converted into kinetic energy.

We can also find this by the formula,

$\sf{}Kinetic\ energy=\dfrac{1}{2}mv^2$

We don’t know v^2 which the velocity square of the object just befot hitting the ground, so let’s find out it by third equation of motion,

$\sf{}\implies v^2=u^2+2as$ [a is same as g]

$\sf{}\implies v^2=0^2+2\times 10\times 5$

$\sf{}\implies v^2=100$

So,velocity^2 is equal to 100.

Let’s put all the values and solve it to find the kinetic energy just before hitting the ground.

$\sf{}\implies Kinetic\ energy=\dfrac{1}{2}\times 10\times 100$

$\sf{}\implies Kinetic\ energy=\dfrac{1}{2}\times 1000$

$\sf{}\implies Kinetic\ energy=\dfrac{1}{1}\times 500J$

$\sf{}\sf{}\implies Kinetic\ energy= 500J$

Therefore,kinetic energy just before hitting the ground is equal to 500J