Answer:
a. 12.57 m/s b. 39.5 m/s² c. Her centripetal force is four times her weight.
Explanation:
a. What is Missy's linear speed on the rotor?
Missy's linear speed v = 2πr/T where r = radius = 4.0 m and T = time it takes to complete one revolution = 2.0 s
So, v = 2πr/T
= 2π(4.0 m)/2.0 s
= 4π m/s
= 12.57 m/s
b. What is Missy's centripetal acceleration on the rotor?
Missy's centripetal acceleration, a = v²/r where v = linear velocity = 12.57 m/s and r = radius = 4.0 m
a = v²/r
= (12.57 m/s)²/4.0 m
= 158.01 m²/s² ÷ 4.0 m
= 39.5 m/s²
c. If her mass is 50-Kg, how is the centripetal force compare to her weight?
Her centripetal force F = ma where m = mass = 50 kg and a = centripetal acceleration = 39.5 m/s².
Her weight W = mg where m = mass = 50 kg and g = acceleration due to gravity = 9.8 m/s².
So, comparing her centripetal force to her weight, we have
F/W = ma/mg
= a/g
= 39.5 m/s² ÷ 9.8 m/s²
= 4.03
≅ 4
So her centripetal force is four times her weight.
Given that :
Power (P) = 30 W ,
time (t) = 40 s,
Work = ?
we know that, power is defined as rate of doing work
Power = Work ÷ time
=> Work = Power × time
= 30 × 40
<em> W = 1200 J</em>
Answer:
The easiest way to tackle this problem is by breaking the vectors up into their components (also it's easier to type this method).
G = 40.3 cos (-35.0°) i + 40.3 sin (-35.0°) j ----where i denotes the x direction and j denotes the y direction
H = 63.3 sin (270°) j ----- I left off the i component because i know cos 270 is 0.
40.3 and 63.3 are the magnitudes of your vector, or the hypotenuse of a triangle. We are finding the horizontal (Adjacent) and vertical (Opposite) legs the respective hypotenuse (we have to remember SOH COH TOA)
Now you can simply add components
G + H = (40.3 cos (-35.0)) i + (40.3 sin (-35.0°)+ 63.3 sin (270)) j ----be sure to pay close attention to signs when doing your calculations on your calculator.
Answer: the atmospheric pressure is generally expressed in terms of the height of the mercury column.at normal temperature and pressure, the barometric height is 760mm at sea level which is taken as one atmosphere. thus atmospheric pressure is also expressed in a unit atmosphere where 1 atm= 0.76m of hg. 9