Question

A vase with a mass of 0.800 kilograms falls from a height of 0.750 meters to a position of 0.500 meters above the floor. Ignoring frictional effects, the kinetic energy at the 0.500 position is _____.

Answer 1

Answer:

The kinetic energy at the 0.500 position is 1.96 J.

Explanation:

Mass of the vase = 0.800 kg

Height from where vase fallen = 0.750 m

Potential energy of vase at 0.750 m:

$P.E=mgh=0.800 kg\times 9.8 m/s^2 \times 0.750 m=5.88 Joules$

Kinetic energy of the vase at the point just before it was about to fell:

$K.E=0 J$ (absence of motion)

P.E + K.E = 5.88 J + 0 J = 5.88 Joules

Potential energy of vase at 0.500 m:P.E'

$P.E=mgh=0.800 kg\times 9.8 m/s^2 \times 0.500 m=3.92 Joules$

Kinetic energy of the vase at the point 0.500 m above the floor: K.E'

As we know, that sum of P.E and K.E remains constant.;

P.E' + K.E' = 3.92 J + K.E' = 5.88 J

K.E' = 5.88 J - 3.92 J = 1.96 J

The kinetic energy at the 0.500 position is 1.96 J.

Answer 2

Answer: The kinetic energy of vase at 0.500 m position is 1.96 J

Explanation:

Law of conservation of energy states that energy can neither be created nor be destroyed but it can only be transformed from one form to another form.

Here, the potential energy of the vase is getting converted into kinetic energy of the vase

So, calculating the potential energy of vase, we use the equation:

P = mgh

where,

m = mass of vase = 0.800 kg

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

h = height of vase = (0.750 - 0.500) m = 0.250 m

Putting values in above equation, we get:

$P=0.800kg\times 9.8m/s^2\times 0.250m\\\\P=1.96J$

At 0.500 m, the potential energy gets converted to kinetic energy.

Kinetic energy of the vase = 1.96 J

Hence, the kinetic energy of vase at 0.500 m position is 1.96 J