A BALL OF MASS 8KG FALLS FROM REST FROM A HIGHT OF 100M NEGLECTING AIR RESISTANCE CALCULATE THE TOTAL ENERGY AFTER FALLING A DISTANCE OF 40M
TE = Total energy.
TE = PE + KE.
TE = M*g*h + 0 = 8*9.8*100 = 7840 Joules @ 100m.
V^2 = Vo^2 + 2g*d = 0 + 19.6*40 = 784,
V = 28 m/s.
TE = Mgh + KE = 8*9.8*60 + 0.5*8*28^2 = 7840 J. @ 60m.
Yes, there is no change in TE.
To calculate the total energy of the ball after falling a certain distance, we need to consider both its potential energy and kinetic energy.
1. Potential energy:
The potential energy of an object raised above the ground is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height above the chosen reference point.
Considering the ball's mass (m = 8 kg) and the initial height (h = 100 m), the potential energy at the beginning is:
PE1 = mgh = 8 kg × 9.8 m/s^2 × 100 m
2. Kinetic energy:
The kinetic energy of an object in motion is given by the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
To find the velocity (v) of the ball after falling a certain distance, we need to use the principle of conservation of energy. The potential energy at the beginning (PE1) will convert entirely into kinetic energy (KE) after falling a certain distance. So, we can equate the potential energy at the beginning to the sum of the potential energy at the new height (PE2) and the kinetic energy (KE).
PE1 = PE2 + KE
Rearranging the equation, we get:
KE = PE1 - PE2
Now, let's calculate PE2:
PE2 = mgh2, where h2 is the new height (distance fallen after 40 m). Since the ball fell from 100 m, the new height (h2) is obtained by subtracting 40 m from the initial height:
h2 = 100 m - 40 m
Once you find the value of h2, you can calculate PE2 using the formula mentioned above.
Finally, substitute the values into the equation for KE and calculate it. The total energy will then be the sum of the potential energy (PE2) and kinetic energy (KE).
at the start, Total Energy = mgh = 800g
energy is conserved, so it does not change
oh, you can go through the steps of finding its PE and KE at 60m, but it will come out the same.
PE = 8*60g = 480g
It falls for t = √(80/g) seconds, at which time its velocity is
v = gt = √(80g)
Then its KE = 1/2 mv^2 = 4(√80g)^2 = 320g
PE+KE is still 800g