Question

Give complete solutions for each of the following problems. All answers must contain the appropriate number of significant figures and the units must be given.

1) You take an elevator from the ground floor to the top of the Empire State Building, a building 102 stories high.

a) What is the work done on you by gravity? (Assume that your mass is 84.0 kg and that the height of the Empire State building is 300 m.)

b) Estimate the amount of work the normal force of the floor did on you.

c) If it takes two minutes to ride the elevator to the top, estimate the average power of the force of gravity.

Answer 1

a) Work done is given by: F*s*cos, where F is magnitude of force vector, s is magnitude of displacement vector, is angle between force and displacement vector.

Here,F=mg downwards, where m is mass, g is gravitational acceleration

= 84*9.8 = 823.2 N.

Also, s = 300 m , upwards

So,=180 degrees as force is downwards while displacement is upwards.

So, work done = 823.2*300*cos180 = - 246960 J

b) Normal force = gravtational force = 823.2 N.

However, normal force is acting upwards.

Also, s = 300 m , upwards

So,=0 degrees as force is upwards and displacement is also upwards.

So, work done = 823.2*300*cos0 = 246960 J

c)Time taken = 2minutes = 2*60 =120 seconds.

Work done by gravity = - 246960 J (found in part (a) )

No,power=work/time = - 246960/ 120 = -2058 W