Question

. A 1 kg ball is thrown upwards with a speed of 9.9 m/s. Calculate the work done

by its weight in one second.​

Answer 1

Given :-

Mass of the ball = 1 kg

Initial velocity of the ball = 9.9 m/s

Time taken by the ball = 1 sec

To Find :-

The work done by its weight in one second.​

Analysis :-

Here we are given with the mass, initial velocity and the time taken by the ball.

Using the second equation of motion substitute the given values from the question and find the displacement accordingly.

Then substitute the values we got in the formula of potential energy and find the work done.

Solution :-

We know that,

• u = Initial velocity
• g = Gravity
• t = Time
• a = Acceleration
• s = Displacement

Using the formula,

$\underline{\boxed{\sf Second \ equation \ of \ motion=ut+\dfrac{1}{2} at^2 }}$

Given that,

Initial velocity (u) = 9.9 m/s

Time (t) = 1 sec

Gravity (g) = 9.8 m/s

Substituting their values,

$\sf 9.9 \times 1 +\dfrac{1}{2} \times 9.8 \times 1^2$

$\sf s = 9.9 + \dfrac{9.8}{2}$

$\sf s = 9.9 + 4.9$

$\sf s=14.8 \ m$

Using their values,

$\underline{\boxed{\sf Potential \ energy=Mass \times Gravity \times Height }}$

Given that,

Mass (m) = 1 kg

Gravity (g) = 9.8 m/s

Height (h) = 14.8 m

Substituting their values,

⇒ w = 1 × 9.8 × 14.8

⇒ w = 145.04 J

Therefore, the work done by it's weight in one second is 145.04 J.

Answer 2

Answer:

Given :-

Mass of the ball = 1 kg

Initial velocity of the ball = 9.9 m/s

Time taken by the ball = 1 sec

To Find :-

The work done by its weight in one second.

Analysis :-

Here we are given with the mass, initial velocity and the time taken by the ball.

Using the second equation of motion substitute the given values from the question and find the displacement accordingly.

Then substitute the values we got in the formula of potential energy and find the work done.

Solution :-

We know that,

u = Initial velocity

g = Gravity

t = Time

a = Acceleration

s = Displacement

Using the formula,

\underline{\boxed{\sf Second \ equation \ of \ motion=ut+\dfrac{1}{2} at^2 }}

Second equation of motion=ut+

2

1

at

2

Given that,

Initial velocity (u) = 9.9 m/s

Time (t) = 1 sec

Gravity (g) = 9.8 m/s

Substituting their values,

\sf 9.9 \times 1 +\dfrac{1}{2} \times 9.8 \times 1^29.9×1+

2

1

×9.8×1

2

\sf s = 9.9 + \dfrac{9.8}{2}s=9.9+

2

9.8

\sf s = 9.9 + 4.9s=9.9+4.9

\sf s=14.8 \ ms=14.8 m

Using their values,

\underline{\boxed{\sf Potential \ energy=Mass \times Gravity \times Height }}

Potential energy=Mass×Gravity×Height

Given that,

Mass (m) = 1 kg

Gravity (g) = 9.8 m/s

Height (h) = 14.8 m

Substituting their values,

⇒ w = 1 × 9.8 × 14.8

⇒ w = 145.04 J

Therefore, the work done by it's weight in one second is 145.04 J.