A ball of mass 8kg falls from rest from a height of 100 m. Neglecting air resistance, calculate it's total energy after falling a house
The total energy of the ball is the sum of its potential energy (PE) when it was at the top and its kinetic energy (KE) after falling:
PE = mgh
PE = 8 x 9.81 x 100
PE = 7848 J
The kinetic energy of the ball can be calculated using the formula:
KE = 1/2mv^2
Where m = mass of the ball, and v = velocity of the ball at a given point.
Since the ball fell from rest, its velocity at the bottom of the house can be calculated using:
v^2 = 2gh
v^2 = 2 x 9.81 x 100
v^2 = 1962
v = sqrt(1962)
v = 44.3 m/s
Now we can calculate the kinetic energy:
KE = 1/2 x 8 x (44.3)^2
KE = 7847.6 J
Therefore, the total energy of the ball after falling the house is:
Total energy = KE + PE
Total energy = 7847.6 J + 7848 J
Total energy = 15695.6 J
Hence, the total energy of the ball after falling the house is 15695.6 J.
The answer is not clear please
I apologize for the confusion in my previous answer. Here's a more detailed explanation:
The ball of mass 8kg has potential energy stored in it due to its position with respect to the ground. When it is at the top of the house, it is at a height of 100m, and this height gives it potential energy, which can be calculated using the formula:
PE = mgh
Where m is the mass of the ball, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the ball from the ground. Therefore, the potential energy of the ball when it is at the top of the house is:
PE = 8 x 9.81 x 100 = 7848 J
When the ball falls from the top of the house and reaches the bottom of the house, it gains kinetic energy due to its motion. The kinetic energy of the ball can be calculated using the formula:
KE = 1/2mv^2
Where m is the mass of the ball, and v is its velocity at the bottom of the house. We can use the formula:
v^2 = 2gh
Where g is the acceleration due to gravity and h is the height that the ball has fallen. In this case, the height that the ball has fallen is 100m. Therefore, we can calculate the velocity of the ball when it reaches the bottom of the house:
v^2 = 2 x 9.81 x 100
v^2 = 1962.2
v = √1962.2
v = 44.3 m/s
Now we can calculate the kinetic energy of the ball:
KE = 1/2 x 8 x (44.3)^2
KE = 7847.6 J
Therefore, the total mechanical energy of the ball at the bottom of the house is:
Total energy = PE + KE
Total energy = 7848 J + 7847.6 J
Total energy = 15,695.6 J
Hence, the total energy of the ball after falling the house is 15,695.6 J.
How do we get 9.81
9.81 m/s^2 is the acceleration due to gravity at the surface of the Earth. It is a constant value that represents the acceleration of any object due to the gravitational force of the Earth. This value is commonly used in physics calculations involving objects on or near the surface of the Earth. It is also known as the standard gravitational acceleration or the acceleration of free fall.
I don't understand the formula used in finding the velocity
The formula used to find the velocity of a falling object near the surface of the Earth is:
v^2 = 2gh
Where v is the final velocity of the object when it hits the ground, g is the acceleration due to gravity, and h is the height from which the object is dropped.
This formula is derived from the equations of motion that govern the motion of a falling object in the absence of air resistance. If we assume that there is no air resistance, then the only force acting on the object is the force due to gravity, which causes the object to accelerate towards the ground at a rate of g. Using this concept, we can derive the above formula.
At the start of the fall, the object has an initial velocity of 0 m/s. As the object falls, it accelerates towards the ground at a rate of g. After falling a distance h, the object reaches a final velocity of v. Using the equations of motion, we can relate the distance fallen, the final velocity, the initial velocity, and the acceleration due to gravity as follows:
v^2 = u^2 + 2gh
Where u is the initial velocity, which is 0 in this case. Therefore, the equation simplifies to:
v^2 = 2gh
This formula allows us to calculate the final velocity of a falling object for a given height and acceleration due to gravity, assuming no air resistance.
How do I join this group
Because I want to start from the beginning