Question

what's the kinetic, potential, and mechanical energies at its initial position, at 2.50m above the initial price and at its maximum height ​

Answer 1

a) Kinetic energy: 15 J, potential energy: 0, mechanical energy: 15 J

b) Kinetic energy: 7.65 J, potential energy: 7.35 J, mechanical energy: 15 J

c) Kinetic energy: 0, potential energy: 15 J, mechanical energy: 15 J

Explanation:

a)

The kinetic energy of an object is the energy possessed by an object due to its motion. It is calculated as

$KE=\frac{1}{2}mv^2$

where

m is the mass of the object

v is the speed of the object

At its initial position (on the ground), the initial speed of the object is

v = 10 m/s

Its mass is

m = 0.300 kg

Therefore, the kinetic energy is

$KE=\frac{1}{2}(0.300)(10)^2=15 J$

The potential energy of an object is the energy possessed by an object due to its position in a gravitational field; mathematically,

$PE=mgh$

where

m is the mass of the object

$g=9.8 m/s^2$ is the acceleration due to gravity

h is the height relative to the ground

When the ball is on the ground, h = 0: therefore, the potential energy is zero,

$PE=0$

FInally, the mechanical energy is the sum of the kinetic energy and the potential energy, therefore:

$E=KE+PE=15 J + 0 = 15 J$

b)

In this case, the position of the ball above the ground is

h = 2.50 m

Therefore, the potential energy is:

$PE=mgh=(0.300)(9.8)(2.50)=7.35 J$

The mechanical energy of an object in motion is always constant, if there are no frictional forces (such as air resistance) acting on it, due  to the law of conservation of energy. Therefore, this means that the mechanical energy of the ball at h = 2.50 m is the same as before:

$E=15 J$

Finally, we can now find the kinetic energy of the ball by using the relationship between mechanical energy, potential energy and kinetic energy:

$KE=E-PE=15 - 7.35=7.65 J$

c)

Here we are analyzing the situation when the bal reaches its maximum height.

First of all, we notice that when the ball reaches its maximum height, it changes direction (from going upward to going downward): this means that its velocity at that moment is zero,

v = 0

And therefore, its kinetic energy is also zero:

$KE=0$

Moreover, we also know that the mechanical energy is always conserved, so its value is equal to the value it had before:

$E=15 J$

And therefore now, by using the relationship between the three types of energy, we can find the value of the potential energy when the ball is at its maximum height:

$PE=E-KE=15-0=15 J$

Learn more about kinetic and potential energy:

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