Answer:
v = 14 m/s
Explanation:
given,
radius of dip = 40 m
The passengers in a roller coaster car feel 50% heavier than their true weight.
Apparent weight
![A = W + \dfrac{W}{2}](https://tex.z-dn.net/?f=A%20%3D%20W%20%2B%20%5Cdfrac%7BW%7D%7B2%7D)
![A =\dfrac{3W}{2}](https://tex.z-dn.net/?f=A%20%3D%5Cdfrac%7B3W%7D%7B2%7D)
![A =\dfrac{3mg}{2}](https://tex.z-dn.net/?f=A%20%3D%5Cdfrac%7B3mg%7D%7B2%7D)
When the car is at the bottom, the weight will be acting downwards and the centripetal force will also be acting downward where as Normal force which is apparent weight will be acting in upward direction.
now,
![N = m g + \dfrac{mv^2}{r}](https://tex.z-dn.net/?f=N%20%3D%20m%20g%20%2B%20%5Cdfrac%7Bmv%5E2%7D%7Br%7D)
![\dfrac{3mg}{2} = m g + \dfrac{mv^2}{r}](https://tex.z-dn.net/?f=%5Cdfrac%7B3mg%7D%7B2%7D%20%3D%20m%20g%20%2B%20%5Cdfrac%7Bmv%5E2%7D%7Br%7D)
![\dfrac{mg}{2} = \dfrac{mv^2}{r}](https://tex.z-dn.net/?f=%5Cdfrac%7Bmg%7D%7B2%7D%20%3D%20%5Cdfrac%7Bmv%5E2%7D%7Br%7D)
![v = \sqrt{\dfrac{rg}{2}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cdfrac%7Brg%7D%7B2%7D%7D)
![v = \sqrt{\dfrac{40\times 9.8}{2}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cdfrac%7B40%5Ctimes%209.8%7D%7B2%7D%7D)
v = 14 m/s
Let us say that x is the cut that we will make on the
sides to make a box, therefore the new dimensions are:
l = 15 – 2x
w = 8 – 2x
It is 2x since we cut on two sides.
We know that volume is:
V = l w x
V = (15 – 2x) (8 – 2x) x
V = 120x – 30x^2 – 16x^2 + 4x^3
V = 120x – 46x^2 + 4x^3
Taking the 1st derivative:
dV/dx = 120 – 92x + 12x^2
Set dV/dx = 0 to get maxima:
120 – 92x + 12x^2 = 0
Divide by 12:
x^2 – (92/12)x + 10 = 0
(x – (92/24))^2 = -10 + (92/24)^2
x - 92/24 = ±2.17
x = 1.66, 6
We cannot have x = 6 because that will make our w
negative, so:
x = 1.66 inches
So the largest volume is:
V = 120x – 46x^2 + 4x^3
V = 120(1.66) – 46(1.66)^2 + 4(1.66)^3
V = 90.74 cubic inches
Answer:
Explanation:
Normal length of spring = 28.3 cm
stretched length of spring = 38.2 cm
length of extension = 38.2 - 28.3 = 9.9 cm
= 9.9 x 10⁻² m
force applied to stretch = .55 x 9.8 ( mg )
= 5.39 N
Force constant = force applied / extension
= 5.39 / 9.9 x 10⁻²
= .5444 x 10² N /m
= 54.44 N/m
Elements of art are stylistic features that are included within an art piece to help the artist communicate. The seven most common elements include line, shape, texture, form, space, colour and value, with the additions of mark making, and materiality.
You would create a darker value if you shaded it, shading it makes it darker.
Answer:
Temperature of the gas molecules is 7.96 x 10⁴ K
Explanation:
Given :
Ions accelerated through voltage, V = 10.3 volts
The work done to change the position of singly charged gas ions is given by the relation :
W = q x V
Here q is charge of the ions and its value is 1.6 x 10⁻¹⁹ C.
Average kinetic energy of gas molecules is given by the relation:
K.E. = ![\frac{3}{2}kT](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7DkT)
Here T is temperature and k is Boltzmann constant and its value is 1.38 x 10⁻²³ J/K.
According to the problem, the average kinetic energy of gas is equal to the work done to move the singly charged ions, i.e. ,
K.E. = W
![\frac{3}{2}kT = qV](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7DkT%20%3D%20qV)
Rearrange the above equation in terms of T :
![T= \frac{2qV}{3k}](https://tex.z-dn.net/?f=T%3D%20%5Cfrac%7B2qV%7D%7B3k%7D)
Substitute the suitable values in the above equation.
![T=\frac{2\times1.6\times10^{-19}\times10.3 }{3\times1.38\times10^{-23} }](https://tex.z-dn.net/?f=T%3D%5Cfrac%7B2%5Ctimes1.6%5Ctimes10%5E%7B-19%7D%5Ctimes10.3%20%7D%7B3%5Ctimes1.38%5Ctimes10%5E%7B-23%7D%20%7D)
T = 7.96 x 10⁴ K