Question

Now is the time for some exercise. You decide to do some pushups. In every pushup, you lift center of mass (this is point where you can assume all the mass of an object to be concentrated) of your body by 20 cm. Assume that your mass is 50 kg.
a.How much work you do against gravity in lifting up your body?
b.Now assume that same amount of work is done in lowering your body. What is the total work done in one pushup?
c.If you are doing 15 pushups per minute, what is the power required?
d.How much energy will you spend in 5 minutes of this exercise?

Answer 1

Given :

Mass of body = 50 kg

Height by which centre of mass of the body is lifted up = 20 cm

To Find :

(a) How much work is done  against gravity in lifting up the body?

(b).Now assuming  that same amount of work is done in lowering the body , then what is the total amount of work done in one pushup?

(c). What is the power required to perform 15 pushups per minute ?

(d).Amount  energy spend in 5 minutes of this exercise = ?

Solution ;

Given height in m will be :

= $\frac{20}{100}$ m = 0.2 m

(a) The amount of work done  against gravity in lifting up the body is :

= $mgh$

= $50 \times 10 \times 0.2$

= 100 J

(b) The total work done in 1 pushup is :

= work done in going up + work done in coming down

=100 J + 100 J

= 200 J

(c) Now the total no of pushups in 1 min = 15

So ,total energy required = $15 \times 200 J$

                                            = 3000 J

So, Power required = $\frac{energy }{time }$

                                 = $\frac{3000J}{60sec}$

                                 = 50 W

Hence , 50 W power is required to perform 15 pushups per minute .

(d) Since , energy spent in 1 min = 3000 J

  So , the energy spent in 5 mins = $5 \times 3000$ J

                                                        = 15, 000 J

Hence , 15000 J of energy is required to perform this exercise for 15 mins .