A 63.0-kg man is riding an escalator in a shopping mall. The escalator moves the man at a constant velocity from ground level to the floor above, a vertical height of 4.20 m. What is the work done on the man by (a) the gravitational force and (b) the escalator

Explanation:

Given that,

Mass of man =Mm=63kg

W=mg

W=63×9.81

W=618.03N

g=9.81m/s²

The escalator moves at a constant velocity, then this shows that it is not accelerating, then, a=0m/s²

Height escalator traveled

H=4.2m.

We assume that the weight of the escalator is negligible.

a. Work done by gravity

Work done by gravity is given as

Work done(gravity)=mgh

Since the work is done against gravity, then, g is negative

Then,

Work done(gravity)=-mgh

Work done(gravity)=-63×9.81×4.2

Work done(gravity)=-2595.726J

b. Work done by escalator

Using equation of motion to know the force pulling the escalator upward

ΣF = ma, but a=0

ΣF = 0

Only two force is acting on the in y axis, the Normal force and the weight

N-W=0

N=W

Since W=618.03N

Then, N=618.03

The normal is the force pulling the escalator upward

Then, the work done by escalator is given as

Work done=Force × distance

Work done=618.03×4.2

Work done= 2595.76J

Work done by escalator is 2595.76J

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.