Realizing that she often doesn\'t have her students\' full attention during clas
ID: 1497827 • Letter: R
Question
Realizing that she often doesn't have her students' full attention during class, a professor devises an elaborate device on which to stand while she lectures. (Figure 1) The pulley is placed so that the string makes a 45.0-degree angle with the beam. The beam is uniform, 5.00 meters long, and has weight wb. The professor stands 2.00 meters from the pivot point and has weight wp.
The tension in the rope is T = ((wp)(2)+wb(2.5))/5.5355
If the professor's mass is 60 kilograms and the mass of the beam is 20 kilograms, what is the magnitude of the normal force n exerted by the beam on the professor? Use 10 meters per second squared for the magnitude of the acceleration due to gravity.
n = 290 N
As an incentive to her students, the professor attaches a light basket to the center of mass of the beam and tells them that every student who gets an A on the next test gets to put a ball of mass 4 kilograms into the basket. There are enough students in the class that if a high percentage get A's, the weight of the basket will hoist the professor into the air.
How many students have to get A's on the test to hoist the professor up into the air?
Explanation / Answer
taking g =10m/s^2
wp =60*10=600N
Wb =20*10=200N
T = ((wp)(2)+wb(2.5))/5.5355..........equation 1
T = (600*2+200*2.5))/5.5355
= 307 N
Normal = Wp-T = 600-307 =293 N
Required T for N to become zero = 600 N...putting this value in equation 1
600 = ((wp)(2)+wb(2.5))/5.5355
weight of professor is fixed but effective weight of beam is changing because of addition of ball masses
600 = (600*2+wp*2.5)/5.5355
600*2+wp*2.5 = 600*5.5355=3321.3
wp = (3321.3-1200)/2.5 = 848.52 N
required weigh to be added = 848-200 = 648N
required mass =648/g =64.8 kg
number of students required = 64.8/4 =16.2 students
It means 17 students are required to get A
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