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malfutka [58]
4 years ago
8

A 50 kg bobsled slides down an ice track starting (at zero initial speed) from the top of a(n) 184 m high hill. The acceleration

of gravity is 9.8 m/s 2 . Neglect friction and air resistance and determine the bobsled’s speed at the bottom of the hill. Answer in units of m/s
Physics
1 answer:
Feliz [49]4 years ago
3 0

Answer:

Explanation:

Given

mass of ice m=50\ kg

Height of hill h=184\ m

Neglecting air resistance

As resistance is absent so Energy at top of hill and at the bottom hill is conserved.

Energy at top is equal to Potential Energy

E_T=mgh=50\times 9.8\times 184

Energy at bottom is equal to kinetic energy at bottom

E_B=\frac{1}{2}mv^2

E_T=E_B

50\times 9.8\times 184=\frac{1}{2}\times 50\times v^2

v=\sqrt{2\times 9.8\times 184}

v=60.05\ m/s                          

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Which of the following expressions gives the ratio of the energy density of the magnetic field to that of the electric field jus
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Answer:

(d) \ \ \frac{\mu_o}{\epsilon_o} (\frac{L}{2\pi r*R} )^2

Explanation:

Energy density in magnetic field is given as;

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where;

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Energy density of electric field

U_E = \frac{1}{2}\epsilon E^2

where;

E is electric field strength

Take the ratio of the two fields energy density

\frac{U_B}{U_E} = \frac{1}{2\mu_o} B^2 / \frac{1}{2}\epsilon E^2\\\\\frac{U_B}{U_E} = \frac{B^2}{2\mu_o}  *\frac{2}{\epsilon E^2} \\\\\frac{U_B}{U_E} = \frac{1}{\mu_o \epsilon} (\frac{B^2}{E^2})

\frac{U_B}{U_E} = \frac{1}{\mu_o \epsilon} (\frac{B}{E})^2

But, Electric field potential, V = E x L = IR (I is current and R is resistance)

\frac{U_B}{U_E} = \frac{1}{\mu_o \epsilon} (\frac{B*L}{E*L})^2

Now replace E x L with IR

\frac{U_B}{U_E} = \frac{1}{\mu_o \epsilon} (\frac{B*L}{IR})^2

Also, B = μ₀I / 2πr, substitute this value in the above equation

\frac{U_B}{U_E} = \frac{1}{\mu_o \epsilon} (\frac{\mu_oI*L}{2\pi r* IR})^2

cancel out the current "I" and factor out μ₀

\frac{U_B}{U_E} = \frac{\mu_o^2}{\mu_o \epsilon} (\frac{L}{2\pi r* R})^2

Finally, the equation becomes;

\frac{U_B}{U_E} = \frac{\mu_o}{\epsilon} (\frac{L}{2\pi r*R })^2

Therefore, the correct option is (d) μ₀/ϵ₀ (L /R 2πr)²

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