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Neko [114]
3 years ago
14

imagine you are working as a rollercoaster designer. you are building a ride the top speed of a 65m/s at the bottom of the first

hill. you estimate that the efficiency of the tracks and car are using roughly 50%. how high must your first hill be to reach that top speed?
Physics
1 answer:
polet [3.4K]3 years ago
5 0

Rollercoasters generate speed by converting gravitational potential energy into kinetic energy by taking the cart to the top of a large hill and letting it go. The conversion of a perfectly efficient system would be like so:

PE = KE

and using the formulas for potential and kinetic energy:

mgh = 1/2mv^2.

However, the efficiency of this system is 50%, meaning that the kinetic energy obtained from this conversion would appear as so:

PE=0.5 KE

mgh=0.5(1/2mv^2)

mgh=1/4mv^2.

The masses cancel out, leaving:

gh=1/4v^2

The goal is to achieve 65 m/s, and with Earth’s innate gravity of 9.806 m/s^2, we have:

gh=1/4v^2

(9.806)h=1/4(65)^2

h=107.71 meters

The height of the first hill must be 107.7 meters to generate a speed of 65 m/s with a conversion efficiency of 50%.

Hope this helps!

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A spherical capacitor contains a charge of 3.50 nC when connected to a potential difference of 210.0 V. Its plates are separated
Lelu [443]

Incomplete question as we have not told to find what quantity.The complete question is here

A spherical capacitor contains a charge of 3.50 nC when connected to a potential difference of 210.0 V. Its plates are separated by vacuum and the inner radius of the outer shell is 5.00 cm.calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.

Answer:

(a) C=16.7pF

(b) r_{a} =3.749cm

(c) E=2.24*10^{4} N/C

Explanation:

Given data

Q=3.50nC\\V=210V\\r_{b}=5.0cm

For part (a)

The Capacitance given by:

C=\frac{Q}{V}\\ C=\frac{3.50*10^{-9} C}{210V}\\C=1.6666*10^{-11}F\\or\\C=16.7pF

For part (b)

The Capacitance of coordinates is given as

C=\frac{4\pi e}{\frac{1}{r_{a} }-\frac{1}{r_{b} } }\\ So\\{\frac{1}{r_{a} }-\frac{1}{r_{b} } }=\frac{4\pi *8.85*10^{-12} }{1.666*10^{-11}}=6.672m^{-1} \\ \frac{1}{r_{a} }=6.672+(1 /0.05)\\\frac{1}{r_{a} }=26.672\\r_{a} =1/26.672\\r_{a} =0.0375m\\r_{a} =3.749cm

For part (c)

The electric field according to Gauss Law is given by:

EA=\frac{Q}{e}\\ E=\frac{Q}{4\pi er_{a}^{2}  }=\frac{kQ}{r_{a}^{2}}\\  E=\frac{9*10^{9}*3.50*10^{-9} }{(0.0375m)^{2} }\\ E=2.24*10^{4} N/C

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Explanation:

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Jupiter is made of gas(like Saturn, Uranus and Neptune). What would happen to the strength of gravity if you
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Answer:

a) The strength of gravity decreases if one moved away from Jupiter

b) The strength of gravity increases if one fell into Jupiter

Explanation:

The gravitational attraction is given by Newton law of gravitation as follows;

Force \ (strength) \ of \ gravity = \dfrac{G \times M \times m}{R^2}

Where;

G = The universal gravitational constant = 6.67408 × 10⁻¹¹ m³/(kg·s²)

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m = The mass of the nearby body

R = The distance between the centers of Jupiter and the body

From the equation, we have that the gravitational strength varies inversely with the square of the separation distance between two bodies

Therefore, as one moves away, R increases, and the strength of gravity reduces

Similarly as the body falls into Jupiter, R, reduces the gravitational strength increases.

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