At a height of 9 meter from ground if a body of mass 2 kg has gravitational potential energy 36 Joule, what
will be its final velocity with which it strikes the ground if it is dropped from there?
6
6 is the answer
Well, let's crunch some numbers and see what we get! Now, the gravitational potential energy of the body is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
So, if we plug in the values, we get 36 = 2 × 9.8 × h. Solving for h, we find that h = 36 / (2 × 9.8) ≈ 1.84 meters.
Now, when the body is dropped, it will lose potential energy and gain kinetic energy. At the moment it hits the ground, all its potential energy will be converted into kinetic energy.
So, the kinetic energy (KE) can be calculated using the formula KE = 1/2 mv^2, where m is the mass and v is the velocity. Since all the potential energy is converted to kinetic energy, we can equate PE to KE.
Therefore, 36 = 1/2 × 2 × v^2. Solving for v, we get v ≈ √(36 × 2 / 2) ≈ √(36) ≈ 6 meters per second.
So, the final velocity of the body when it strikes the ground would be approximately 6 meters per second. But hey, don't forget to account for air resistance and the fact that I'm a clown, not a physicist!
To find the final velocity of the body when it strikes the ground, we can use the principle of conservation of energy.
The potential energy of the body at a height h can be calculated using the formula:
Potential Energy = mass * gravitational acceleration * height
In this case, the potential energy is given as 36 Joules, the mass is 2 kg, and the height is 9 meters. Therefore, we can rewrite the formula as:
36 = 2 * 9.8 * 9
Now, we can solve for the gravitational acceleration:
gravitational acceleration = 36 / (2 * 9)
gravitational acceleration = 2 m/s²
Next, we can use the principle of conservation of energy to calculate the final velocity. At the height of 9 meters, the body only has potential energy. When it strikes the ground, all the potential energy is converted into kinetic energy.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity²
Since the potential energy is converted into kinetic energy, we can equate the two:
Potential Energy = Kinetic Energy
36 = (1/2) * 2 * velocity²
Now, we can solve for the velocity:
velocity² = (2 * 36) / 2
velocity² = 36
Taking the square root of both sides, we get:
velocity = √36
velocity = 6 m/s
Therefore, the final velocity with which the body strikes the ground when dropped from a height of 9 meters is 6 m/s.
K.E. = P.E.
1/2 m v^2 = 36 ... v^2 = 36