Key Equations - CH 1-5 Flashcards
25) The curved section of speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the speedway banked?
A) 32°
B) 34°
C) 30°
D) 28°
E) 26°
A) 32
tanꬾ = v˳²/Rg
= (34)²/190 x 9.8
=.621
ꬾ= 31.83°
24) A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?
A) 29.1°
B) 13.5°
C) 33.8°
D) 56.2°
E) 60.9°
A) 29.1
Ncos ꬾ= mg
Nsinꬾ = mv²/r
tanꬾ = v²/rg = 24.5 m/s)²/(110 m)(9.8 m/s²)
ꬾ = 29.1°
23) A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can be reduced or even eliminated. How long should each rotation take for a doughnut-shaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of Earth?
A) 91 min
B) 8.7 min
C) 4.6 min
D) 1.5 min
E) 0.011 min
D) 1.5 min
centrip acc = (1/10) g = 0.980m/s2
.
centrip acc = ω2 r
.
0.980 = ω2 *200
.
ω = 0.07 radians persecond
.
time for one rotation = distance / speed = 2π radians / 0.07 rad persec = 89.76 seconds or 1.5 mins (period of rotation)
22) A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second unbanked curve of radius 320 m if the coefficient of static friction between the car’s tires and the road surface is the same in both cases?
A) 160 m/s
B) 80 m/s
C) 70 m/s
D) 40 m/s
E) 30 m/s
D) 40 m/s
When r = 80 m and v = 20 m/s, obtain
u= 920M/S)^2/ (80m) (9.8 m/s^2) = 0.51
When r = 320 m and μ remains the same, obtain
(v x m/s)^2/(320m)(9.8 m/s^2)= 0.51
v^2= 1.6 x 10^3
v = 40 m/s
20) In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top of a vertical circle with a radius of 2.5 km?
A) 79 m/s
B) 310 m/s
C) 260 m/s
D) 160 m/s
E) 510 m/s
D. 160 m/s
In a vertical circle, at the very top, the only force would be the force of gravity, there is no normal.
Therefore, the force of gravity must equal Fc
mg=mac
masses cancel out. ac= V2/r
g=v2/r
156.52 m/s
19) Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s. What is the apparent weight of the 70-kg pilot at that point?
A) 3300 N
B) 690 N
C) 2600 N
D) 490 N
E) 1400 N
A)3300 N
radius of the vertical circle, r = 600 m
speed of the plane, v = 150 m/s
mass of the pilot, m = 70 kg
Weight of the pilot due to his circular motion;
W= Fv
Fv= mv^2/r
Fv=70x150^2/600
Fv= 2625N
Real weight of the pilot;
Wr=mg
Wr=70x9.8
Wr= 686 N
Apparent weight - Real weight of pilot = weight due to centripetal force
Fn-mg= mv^2/r
Fn= mv^2/r +mg
Fn= 2625 N+ 686 N
Fn= 3311N
17) A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion?
R = 5m , T = 8sec weight =670N
V = ω × R
V = (2π/(8))×R
V = 3.928m/s
M = 670/(9.8) = 68.367kg
Wapp = W + Mv2/R
Wapp = 670 + ((68.367)(3.928)2/(5))
Wapp = 880N (approx.)
18) A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. The car maintains its speed over the bump. What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the top of the bump?
A) 200 N
B) 390 N
C) 790 N
D) 490 N
E) 590 N
r = 30 m
v = 10 m/s
m = 60 kg
(a) Let N be the normal reaction.
At the bump
N = mg - mv^2 / r
N = 60 x 9.8 - 60 x 10 x 10 / 30 = 588 - 200 = 388 newton
Kepler’s Third Law: the square of the period of a planet is proportional to the cube of the average orbital radius
Velocity of a orbiting satellite
Radius of a satellite orbiting earth
Newton’s Law of Universal Gravitation
Newton’s Law of Universal gravitation (finding radius)
According to the equation below, as orbital radius ________ (increases/decreases) the acceleration due to gravity (increases/decreases), velocity (increase, decrease), and period (increases/decreases))
25) The curved section of speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the speedway banked?
A) 32°
B) 34°
C) 30°
D) 28°
E) 26°
A) 32
tanꬾ = v˳²/Rg
= (34)²/190 x 9.8
=.621
ꬾ= 31.83°
