A ball of mass 8kg falls from rest from a height of 100m neglecting air resistance. Calculate its kinetic energy after falling a distance of 30m(take g=10m/s^2).
Vf^2 = Vo^2 + 2g*d.
Vf^2 = 0 + 20*30 = 600.
Vf = 24.5 m/s. = Final velocity.
KE = 0.5m*V^2 = 4*(24.5)^2 = 2400 J.
PE at 100m=mgh
=2*10*100
=20*100
=2000J
PE at 30m=mgh
=2*10*30
=20*30
=600J
total energy at 30m=PE KE
2000=600 KE
2000-600=KE
KE=2000-600
KE=1400J
=14kj
PE max = Mg*hmax = 80*100 = 8000 J.
At ht. of 100 m, KE = 0; PE = 8000 J.
KE + PE = 0 + 8000 = 8000 J.
At ht. of 70 m. above gnd.
PE = Mg*h = 80*70 = 5600 J.
KE + PE = 8000
KE + 5600 = 8000
KE = 8000-5600 = 2400 J.
A ball of mass 8kg falls from rest from a height of 100m neglecting air resistance. Calculate it's kinetic energy after falling a distance of 30m (take g=10 miter per second square)
To calculate the kinetic energy (KE) of the ball after falling a certain distance, we can use the concept of conservation of energy.
The total mechanical energy of the ball is conserved throughout its motion, i.e., the sum of its potential energy (PE) and kinetic energy (KE) remains constant.
The potential energy of an object at height h is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (which is 10 m/s^2 in this case), and h is the height.
Initially, when the ball is at a height of 100m, its potential energy is given by PE1 = mgh1.
Finally, when the ball falls to a height of 30m, its potential energy is given by PE2 = mgh2.
As there is no air resistance, there is no energy lost due to work done against it. Therefore, the total initial potential energy of the ball (PE1) is equal to the final kinetic energy (KE2).
So, PE1 = KE2
Using the formula for potential energy, we have:
mgh1 = KE2
Substituting the given values:
(8kg)(10m/s^2)(100m) = KE2
KE2 = 8000 Joules
Therefore, the kinetic energy of the ball after falling a distance of 30m is 8000 Joules.