Physics, 08.04.2020 01:30 Valduarte07

While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find themotion somewhat unpleasant. To take your mind off your stomach, youwonder about the motion of the ride. You estimate the radius of thebig wheel to be 15 , and you use your watch tofind that each loop around takes 25 .

a. What is your speed?
b. What is the magnitude of your acceleration?
c. What is the ratio of your weight at the top of the ride to yourweight while standing on the ground?
d. What is the ratio of your weight at the bottom of the ride toyour weight while standing on the ground?

Answers: 3

Show answers

Answers

Answer from: lindsaypre0644

a. 0.0628 m

b. 0.000263 m/s2

c.99.997%

d.100.003%

Explanation:

Suppose the radius is 15 m and each loop takes 25 minutes (25*60 = 1500 seconds) to complete. The circumference of the Ferris wheel would be

C = 2πR = 2π*15 = 94.25 m

The your speed is the length of each loop per unit of time to complete each loop

v = C/t = 94.25 / 1500 = 0.0628 m/s

b. Since the circular motion is constant, the only acceleration from the motion is the centripetal acceleration, which can be calculated as the following:

a_c = v^2/r = 0.0628^2/15 = 0.000263 m/s^2

c. Let g = 9.8 m/s^2. At top of the ride, the centripetal acceleration would be pushing you up, while gravity pushes you down, so the weight you experience (compare to standing on ground would be):

$\frac{g-a_c}{g} = \frac{9.8 - 0.000263}{9.8} = 0.99997 = 99.997 \%$

d. At the bottom of the ride, both centripetal acceleration and gravity would be pushing you downward, making you feel like

$\frac{g+a_c}{g} = \frac{9.8 + 0.000263}{9.8} = 1.00003 = 100.003 \%$

Answer from: aletadaboss

a) The speed is 3.77 m/s

b) The acceleration is 0.948 m/s²

c) The ratio of your weight at the top to your weight standing on the ground is 0.903

d) The ratio of your weight at the bottom of the ride to your weight while standing on the ground is 1.097

Explanation:

a) The speed of the wheel is equal to:

v=rw

Where

r = radius of the circle = 15 m

w = angular velocity

$w=\frac{2\pi }{T}$

$v=\frac{2\pi r}{T} =\frac{2\pi *15}{25} =3.77m/s$

b) The acceleration is:

$a=\frac{v^{2} }{r} =\frac{3.77^{2} }{15} =0.948m/s^{2}$

c) Applying the Newton´s second law:

$W_{true} -N=ma\\W_{true}-N=\frac{mv^{2} }{r} \\N=W_{app} =W_{true}-\frac{mv^{2} }{r}$

Dividing the expression by Wtrue:

$\frac{W_{app}}{W_{true} } =1-\frac{mv^{2} }{rW_{true}} \\\frac{W_{app}}{W_{true} }=1-\frac{v^{2} }{rg} =1-\frac{3.77^{2} }{15*9.8} =0.903$

d) Applying the Newton´s second law:

$N-W_{true}=ma\\N-W_{true}=\frac{mv^{2} }{r} \\N=W_{app} =W_{true}+\frac{mv^{2} }{r}$

Dividing the expression by Wtrue:

$\frac{W_{app}}{W_{true} } =1+\frac{mv^{2} }{rW_{true}} \\\frac{W_{app}}{W_{true} }=1+\frac{v^{2} }{rg} =1+\frac{3.77^{2} }{15*9.8} =1.097$

Answer from: Quest

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

Answer from: Quest

harry byrd declared organized resistance by southern states would prevent racial integration.