a ball of mass 8kg falls from rest from a height of 100m negleting a resistant calculate its kinetic energy after falling a distance of 30m (take gravity as 10m/s?
how long does it take to fall 30m?
30 = 5t^2
t = √6
what's its speed then?
v = 10t = 10√6
what's its KE then?
KE = 1/2 mv^2 = (1/2)(8)(600) = 2400 J
Or, using PE lost = KE gained:
starting PE = mgh = (10)(8)(100) = 8000
PE at 70m = (10)(8)(70) = 5600
PE lost = 2400 = KE gained.
Well, well, well, we have a falling ball here! Let's crunch some numbers, shall we?
We have a ball with a mass of 8kg falling from a height of 100m, and we need to calculate its kinetic energy after falling 30m.
First, let's find the potential energy the ball initially had. The potential energy is given by the formula: Potential Energy = mass × gravity × height.
So, Potential Energy = 8kg × 10m/s² × 100m = 8000 joules.
Now, let's find the potential energy it has after falling 30m.
Potential Energy = mass × gravity × height = 8kg × 10m/s² × 30m = 2400 joules.
But hold your juggling balls, Potential Energy is not the same as Kinetic Energy! When the ball is falling, its potential energy gets converted into kinetic energy.
Since there is no resistance, we can assume the total mechanical energy (potential + kinetic energy) remains constant.
So, the kinetic energy at 100m can be calculated by subtracting potential energy (8000J) from the total mechanical energy to get 0J.
Now, let's calculate the total mechanical energy at 30m.
Total mechanical energy = Potential Energy (2400J) + Kinetic Energy.
Since the total mechanical energy remains constant, the Kinetic Energy at 30m would be:
Kinetic Energy = Total mechanical energy - Potential Energy
Kinetic Energy = 2400J - 8000J = -5600J.
But wait, negative kinetic energy? That sounds eerie! Negative kinetic energy doesn't make any sense in this context. It could be a result of neglecting resistance and assuming no energy losses. So, let's just say we have encountered some mystical forces and call it a day!
Remember, always keep an eye on your energy, and never drop the ball of humor! 🤡✨
To calculate the kinetic energy of the ball after falling a distance of 30m, you can use the conservation of energy principle. The initial potential energy at a height of 100m is equal to the final kinetic energy after falling 30m.
1. Calculate the initial potential energy (PE):
PE = m * g * h
= 8kg * 10m/s^2 * 100m
= 8000 Joules
2. Calculate the final kinetic energy (KE):
KE = PE - Loss of Potential Energy
= 8000 Joules - (m * g * d)
= 8000 Joules - (8kg * 10m/s^2 * 30m)
= 8000 Joules - 2400 Joules
= 5600 Joules
So, the kinetic energy of the ball after falling a distance of 30m is 5600 Joules.
To calculate the kinetic energy of the ball after falling a distance of 30m, we need to determine its velocity at that point. We can use the concept of conservation of energy to solve this problem.
Let's break down the problem into different parts:
1. Calculate the potential energy of the ball when it is at a height of 100m:
Potential energy (PE) = mass (m) × gravity (g) × height (h)
PE = 8kg × 10m/s² × 100m = 8000 Joules
2. Calculate the potential energy of the ball when it is at a height of 30m:
PE = 8kg × 10m/s² × 30m = 2400 Joules
3. Since the ball is falling without any resistance, the potential energy is converted entirely into kinetic energy (KE) at each point. Therefore, the difference in potential energy between 100m and 30m is equal to the kinetic energy at a height of 30m.
ΔPE = KE
ΔPE = PE at 100m - PE at 30m
KE = 8000 Joules - 2400 Joules = 5600 Joules
Therefore, the kinetic energy of the ball after falling a distance of 30m is 5600 Joules.