Question

an object of mass 20kg is dropped from a height of 4m. Fill in the blanks in the following table by computing the potential energy and kinetic energy in each case
1m, 2m, 3m and 4m​

Answer 1

Answer:

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Explanation:

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Answer 2

Question:

An Object of mass 20 kg falls from a height of 4 m. Taking g = 10 ${m/s^{2} }$, Fill the following table -

Given:

Mass of the object = m = 20 kg

Acceleration due to gravity = g = 10 $m/s^{2}$

Solution:

At a Height of 4 m

Since the object is just dropped,

The velocity of the ball = 0 m/s

             Potential Energy                         |               Kinetic Energy

 Potential Energy = m x g x h                   |  Kinetic Energy = $\frac{1}{2}$ $mv^{2}$

                         $E_{p}$ = 20 x 10 x 4                |                      $E_{k}$ = $\frac{1}{2}$ x 20 x $0^{2}$

                         $E_{p}$ = 800 J                         |                      $E_{k}$ = 0 J

Total Energy = $E_{p} + E_{k}$

                      = 800 + 0

                      = 800 J

At a Height of 3 m

To find Potential Energy, we need height

To find Kinetic Energy, we need velocity  

Finding Velocity

Initial velocity = u = 0 m/s                         (Velocity at Highest Point is 0)

Acceleration = a = g = 10 m/s

Distance Travelled = s = 4-3

                                = 1 m

We know u, a, and s,

We can find v using the third equation of motion

         $v^{2} - u^{2} = 2as$

         $v^{2} - 0 =$ 2 x 10 x 1

          $v^{2} = 20$

Finding Potential and Kinetic Energy

             Potential Energy                         |               Kinetic Energy

 Potential Energy = m x g x h                   |  Kinetic Energy = $\frac{1}{2}$ $mv^{2}$

                         $E_{p}$ = 20 x 10 x 3                |                      $E_{k}$ = $\frac{1}{2}$ x 20 x 20

                         $E_{p}$ = 600 J                         |                      $E_{k}$ = 200  J

Total Energy = $E_{p} + E_{k}$

                      = 600 + 200

                      = 800 J

At a Height of 2 m,

To find Potential Energy, we need height

To find Kinetic Energy, we need velocity  

Finding Velocity

Initial velocity = u = 0 m/s                         (Velocity at Highest Point is 0)

Acceleration = a = g = 10 m/s

Distance Travelled = s = 4-2

                                = 2 m

We know u, a, and s,

We can find v using the third equation of motion

         $v^{2} - u^{2} = 2as$

         $v^{2} - 0 =$ 2 x 10 x 2

          $v^{2} = 40$

Finding Potential and Kinetic Energy

             Potential Energy                         |               Kinetic Energy

 Potential Energy = m x g x h                   |  Kinetic Energy = $\frac{1}{2}$ $mv^{2}$

                         $E_{p}$ = 20 x 10 x 2                |                      $E_{k}$ = $\frac{1}{2}$ x 20 x 40

                         $E_{p}$ = 400 J                         |                      $E_{k}$ = 400  J

Total Energy = $E_{p} + E_{k}$

                      = 400 + 400

                      = 800 J

At a Height of 1 m,

To find Potential Energy, we need height

To find Kinetic Energy, we need velocity  

Finding Velocity

Initial velocity = u = 0 m/s                         (Velocity at Highest Point is 0)

Acceleration = a = g = 10 m/s

Distance Travelled = s = 4-1

                                = 3 m

We know u, a, and s,

We can find v using the third equation of motion

         $v^{2} - u^{2} = 2as$

         $v^{2} - 0 =$ 2 x 10 x 3

          $v^{2} = 60$

Finding Potential and Kinetic Energy

             Potential Energy                         |               Kinetic Energy

 Potential Energy = m x g x h                   |  Kinetic Energy = $\frac{1}{2}$ $mv^{2}$

                         $E_{p}$ = 20 x 10 x 1                |                      $E_{k}$ = $\frac{1}{2}$ x 20 x 60

                         $E_{p}$ = 200 J                         |                      $E_{k}$ = 600  J

Total Energy = $E_{p} + E_{k}$

                      = 200 + 600

                      = 800 J

Just above the ground (h ≋ 0 m),

To find Potential Energy, we need height

To find Kinetic Energy, we need velocity  

Finding Velocity

Initial velocity = u = 0 m/s                         (Velocity at Highest Point is 0)

Acceleration = a = g = 10 m/s

Distance Travelled = s = 4-0

                                = 4 m

We know u, a, and s,

We can find v using the third equation of motion

         $v^{2} - u^{2} = 2as$

         $v^{2} - 0 =$ 2 x 10 x 4

          $v^{2} = 80$

Finding Potential and Kinetic Energy

             Potential Energy                         |               Kinetic Energy

 Potential Energy = m x g x h                   |  Kinetic Energy = $\frac{1}{2}$ $mv^{2}$

                         $E_{p}$ = 20 x 10 x 0               |                      $E_{k}$ = $\frac{1}{2}$ x 20 x 80

                         $E_{p}$ = 0 J                             |                      $E_{k}$ = 800  J

Total Energy = $E_{p} + E_{k}$

                      = 0 + 800

                      = 800 J

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