Question

7. A machine lifts 120 kg mass from the ground to a height
of 5 m in 3 s. Its average power is :
(a) 1960 W
(b) 19.6 kW
(c) 1.96 MW
(d) 196 W​

Answer 1

Given :-

Mass lifted by the machine = 120 kg

Height of the ground = 5 m

Time taken = 3 sec

To Find :-

The average power.

Analysis :-

Here we are given with the mass, height and time taken.

Firstly, substitute the values given in the question such that the work done is equal to multiplying mass, gravity and height.

In order to find the average power substitute the values we got such that average power is equal to work done by the time taken.

Solution :-

We know that,

• t = Time
• p = Power
• g = Gravity
• h = Height
• m = Mass
• w = Work done

Using the formula,

$\underline{\boxed{\sf Work \ done=Mass \times Gravity \times Height}}$

Given that,

Mass (m) = 120 kg

Gravity (g) = 9.8 m/s

Height (h) = 5 m

Substituting their values,

⇒ w = mgh

⇒ w = 120 × 9.8 × 5

⇒ w = 5880 J

Using the formula,

$\underline{\boxed{\sf Power= \dfrac{Work \ done}{Time \ taken} }}$

Given that,

Work done (w) = 5880 J

Time (t) = 3 sec

Substituting their values,

⇒ p = w/t

⇒ p = 5880/3

⇒ p = 1960 W

Therefore, the average power is 1960 W.

Additional knowledge :-

Work:

Work is defined as force applied to an abject causing it to move from one place to another.

Formula: Work = Force × Displacement

The SI unit of work is the joule (J).

Energy:

Energy is defined as the capacity to perform a work. The work done is equal to mgh which is gained by the object.

Formula: PE = mgh

The SI unit of energy is joules (J).

Power:

Power is defined as the rate at which work is done.

Formula: Power = Work/Time

The unit of power is watt (W).