Question

a stone of mass 0.2 kg is thrown vertically up with a speed of 19.6 m/a. calculate its potential energy and kinetic energy after 1s
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Answer 1

Answer:

Potential energy = 28.812  joules

Kinetic energy = 9.604 joules

Explanation:

Given:

Mass of the stone = m = 0.2 kg

Velocity with which the stone is thrown = u = 19.6 m/s

Time = 1 second

Gravitational force = g = 9.8 m/s²

To find:

• Potential energy
• Kinetic energy

Potential energy:

Potential energy = m×g×h

So, we need to find the height here,

Using second equation of motion which says : $s=ut+\frac{1}{2} at^{2}$

s=19.6×1$+\frac{1}{2} \times -9.8 \times 1 \times 1$

s=19.6-4.9

s=14.7 metres

The stone will travel a distance of 14.7 metres

Potential energy = 0.2×9.8×14.7

Potential energy = 28.812  joules

Kinetic energy:

Here we need to find the value of final velocity (v)

Using third equation of motion:

v²-u²=2as

v²-19.6²=2×-9.8×14.7

v²-384.16= -288.12

v² = -288.12+384.16

v² = 96.04

v = 9.8 m/s

Kinetic energy = $\frac{1}{2}mv^{2}$

Kinetic energy  = 0.5×0.2×9.8×9.8

Kinetic energy  = 0.1×96.04

Kinetic energy = 9.604 joules

Answer 2

Given :

▪ Mass of stone = 0.2kg

▪ Initial velocity = 19.6mps

To Find :

▪ Potential energy and kinetic energy of ball after 1s

Solution :

→ For potential energy, we have to find out height attained by stone after 1s.

→ For kinetic energy, we have to find out final velocity of stone after 1s.

→ Since, acceleration due to gravity is constant throughout the motion, we can easily apply equations of kinematics to solve this type of questions.

✴ Height attained by ball after 1s :

✏ H = ut - (1/2)gt^2

Negative sign shows opposite direction

✏ H = (19.6×1) - (0.5×9.8×1)

✏ H = 19.6 - 4.9

✏ H = 14.7m

✴ Potential energy of ball :

✒ U = mgH

✒ U = 0.2×9.8×14.7

✒ U = 28.812J

✴ Final velocity of ball after 1s :

✏ v^2 - u^2 = -2gH

✏ v^2 - (19.6)^2 = -2(9.8)(14.7)

✏ v^2 - 384.16 = -288.12

✏ v^2 = -288.12 + 384.16

✏ v^2 = 96.04

✏ v = 9.8mps

✴ Kinetic energy of ball :

✒ K = (1/2)mv^2

✒ K = 0.5×0.2×96.04

✒ K = 9.604J