Answer:
My hard pp...............
Explanation:
Answer:
Extraneous
Explanation:
Extraneous variables are any variables that you are not intentionally studying in your experiment or test
Answer:
θ = 14.27°
Explanation:
The only force acting on the puck is the gravitational force. Since the track is banked with an angle θ, we have to separate the components of the weight.
For the sake of simplicity, I will denote the perpendicular direction to the truck as the y-direction, and the direction along the radius as the x-direction.
So, the free-body diagram of the puck is as follows:
1- x-component of the weight of the puck: mgsinθ
2- y-component of the weight of the puck: mgcosθ
3- Normal force in the y-direction perpendicular to the track.
Since there is no motion on the y-direction, normal force is equal to the y-component of the weight of the puck.
The x-component of the weight of the puck is equal to the centripetal force according to Newton's Second Law:
![F = ma\\mg\sin{\theta} = \frac{mv^2}{R}\\\sin{\theta} = \frac{v^2}{gR}](https://tex.z-dn.net/?f=F%20%3D%20ma%5C%5Cmg%5Csin%7B%5Ctheta%7D%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D%5C%5C%5Csin%7B%5Ctheta%7D%20%3D%20%5Cfrac%7Bv%5E2%7D%7BgR%7D)
Substituting the variables given in the question, the angle of the track can be found:
![\sin{\theta} = \frac{(31.9)^2}{(9.8)(421)} = 0.2466\\\theta = 14.27^\circ](https://tex.z-dn.net/?f=%5Csin%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%2831.9%29%5E2%7D%7B%289.8%29%28421%29%7D%20%3D%200.2466%5C%5C%5Ctheta%20%3D%2014.27%5E%5Ccirc)
Answer:
The force on each wire is
![T_1 = 12.5 \ N](https://tex.z-dn.net/?f=T_1%20%20%3D%2012.5%20%5C%20N%20%20)
![T_2 = 25 \ N](https://tex.z-dn.net/?f=%20%20T_2%20%20%3D%20%20%2025%20%5C%20%20N%20%20)
![T_3 = 50 \ N](https://tex.z-dn.net/?f=%20%20T_3%20%20%3D%20%2050%20%20%5C%20%20N%20%20)
Explanation:
From the question we are told that
The acceleration at which the elevator will stop is ![a = \frac{g}{4}](https://tex.z-dn.net/?f=a%20%3D%20%20%5Cfrac%7Bg%7D%7B4%7D)
The weight of each section of the wire is ![W = \ 10 \ N](https://tex.z-dn.net/?f=W%20%3D%20%20%5C%2010%20%5C%20N)
Generally
here
are weight at each section
Generally considering the first section, the force acting along the y-axis is mathematically represented as
![\sum F_y_1 = T_1 - W_1 = m * a](https://tex.z-dn.net/?f=%5Csum%20F_y_1%20%3D%20%20T_1%20-%20W_1%20%3D%20%20m%20%2A%20%20a)
Here
represents the tension on the wire at the first section while
represents the weight of the lamp at the first section
So
![T_1 - 10 = m * \frac{g}{4}](https://tex.z-dn.net/?f=T_1%20%20-%2010%20%3D%20m%20%2A%20%20%5Cfrac%7Bg%7D%7B4%7D)
=> ![T_1 - 10 = \frac{W_1}{4}](https://tex.z-dn.net/?f=T_1%20%20-%2010%20%3D%20%20%5Cfrac%7BW_1%7D%7B4%7D)
=> ![T_1 - 10 = \frac{10}{4}](https://tex.z-dn.net/?f=T_1%20%20-%2010%20%3D%20%20%5Cfrac%7B10%7D%7B4%7D)
=> ![T_1 = 12.5 \ N](https://tex.z-dn.net/?f=T_1%20%20%3D%2012.5%20%5C%20N%20%20)
Generally considering the second section, the force acting along the y-axis is mathematically represented as
![\sum F_y_2 = T_2 -T_1- W_2 = m * a](https://tex.z-dn.net/?f=%5Csum%20F_y_2%20%3D%20%20T_2%20-T_1-%20W_2%20%3D%20%20m%20%2A%20%20a)
=> ![T_2 - T_1- 10 = m * \frac{g}{4}](https://tex.z-dn.net/?f=%20%20T_2%20-%20T_1-%2010%20%3D%20%20m%20%2A%20%20%5Cfrac%7Bg%7D%7B4%7D)
=> ![T_2 - 12.5- 10 = \frac{W_2}{4}](https://tex.z-dn.net/?f=%20%20T_2%20-%2012.5-%2010%20%3D%20%20%20%20%5Cfrac%7BW_2%7D%7B4%7D)
=> ![T_2- 12.5- 10 = \frac{10}{4}](https://tex.z-dn.net/?f=%20%20T_2-%2012.5-%2010%20%3D%20%20%20%20%5Cfrac%7B10%7D%7B4%7D)
=> ![T_2 = 25 \ N](https://tex.z-dn.net/?f=%20%20T_2%20%20%3D%20%20%2025%20%5C%20%20N%20%20)
Generally considering the third section, the force acting along the y-axis is mathematically represented as
![\sum F_y_3 = T_3- T_2 -T_1- W_3 = m * a](https://tex.z-dn.net/?f=%5Csum%20F_y_3%20%3D%20T_3-%20T_2%20-T_1-%20W_3%20%3D%20%20m%20%2A%20%20a)
![T_3 - T_2 - T_1- 10 = m * \frac{g}{4}](https://tex.z-dn.net/?f=%20%20T_3%20-%20T_2%20-%20T_1-%2010%20%3D%20%20m%20%2A%20%20%5Cfrac%7Bg%7D%7B4%7D)
![T_3 - 25 - 12.5- 10 = \frac{W_2}{4}](https://tex.z-dn.net/?f=%20%20T_3%20-%2025%20-%2012.5-%2010%20%3D%20%20%20%20%5Cfrac%7BW_2%7D%7B4%7D)
![T_3 - 25 - 12.5- 10 = \frac{10}{4}](https://tex.z-dn.net/?f=%20%20T_3%20-%2025%20-%2012.5-%2010%20%3D%20%20%20%20%5Cfrac%7B10%7D%7B4%7D)
![T_3 = 50 \ N](https://tex.z-dn.net/?f=%20%20T_3%20%20%3D%20%2050%20%20%5C%20%20N%20%20)