A 15 Kg object that is free falling has a total mechanical energy of 13,230 Joules.
(A) From what height was the object dropped?
(B) What is the velocity of the object when it hits the ground?
(C) How long does the object fall?
m*g*h=13,230
solve for h.
final energy is 1/2 mv^2= 13230 solve for v
how long?
you know the final velcocity, so the average velocity is half that.
time= h/avgvelocity
To answer these questions, we need to use the principles of mechanical energy and free fall motion. Here's how we can approach each question step by step:
(A) To find the height from which the object was dropped, we can use the concept of gravitational potential energy. The total mechanical energy of the object can be given as the sum of its potential energy and kinetic energy. Since the object is dropped (initially not moving), its initial kinetic energy is zero. Therefore, the total mechanical energy at the start of its fall is equal to its potential energy.
The formula to calculate the potential energy of an object near the surface of the Earth is:
Potential Energy = mass * gravity * height
We know the mass of the object is 15 kg, and the gravitational constant near the surface of the Earth is approximately 9.8 m/s^2. Let's substitute these values into the equation and solve for height:
Potential Energy = 13,230 J
Mass = 15 kg
Gravity = 9.8 m/s^2
13,230 J = 15 kg * 9.8 m/s^2 * height
Solving for height:
height = 13,230 J / (15 kg * 9.8 m/s^2)
Calculating the height will give you the answer to part (A).
(B) To find the velocity of the object when it hits the ground, we can use the equation for the final velocity of an object in free fall:
Final Velocity^2 = Initial Velocity^2 + 2 * gravity * height
Since the object is dropped from rest, the initial velocity is zero. We already calculated the height in part (A), so let's substitute these values into the equation and solve for the final velocity:
Final Velocity^2 = 0 + 2 * 9.8 m/s^2 * height
Taking the square root of both sides of the equation will give you the answer to part (B).
(C) To find the time it takes for the object to fall, we can use the equation for the time of flight in free fall:
Time = sqrt((2 * height) / gravity)
We already know the height from part (A) and the gravitational constant. Plugging in these values will give you the answer to part (C).