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4 years ago

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A 39.5 kg child stands at the center of a 125 kg playground merry-go-round which rotates at 3.10 rad/s. If the child moves to th

e edge of the merry-go-round, what is the new angular velocity of the system? Model the merry-go-round as a solid disk

1 answer:

Neporo4naja [7]4 years ago

3 0

Using the law of conservation of angular momentum, we have

<span>I1 w1 = I2 w2 </span>

<span>ie., m1r^2/2 x w1 = ( m1r^2/2 + m2r^2 ) w2 </span>

<span>ie., new angular velocity w2 = m1 w1 / ( m1+ 2m2) = 125 x 3.1 / ( 125 + 2 x39.5 ) </span>

<span>= 1.8995 = 1.9 rad /sec ( nearly )</span>

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A model rocket blasts off and moves upward with an acceleration of 12 m/s2 until it reaches a height of 26 m. at that height, it

Diano4ka-milaya [45]

initial acceleration of rocket is given as

a = 12 m/s^2

h = 26 m

now we can use kinematics to find its speed

$v_f^2 - v_i^2 = 2 a h$

$v_f^2 - 0 = 2 * 12*26$

$v_f = 24.98 m/s$

now after this it will be under free fall

so now again using kinematics

$v_f = 0$

at maximum height

$v_f^2 - v_i^2 = 2 a s$

$0 - 24.98^2 = 2 * (-9.8)* h$

$h = 31.8 m$

total height from the ground = 31.8 + 26 = 57.8 m

Part b)

now after reaching highest height it will fall to ground

So in order to find the speed we can use kinematics again

$v_f^2 - v_i^2 = 2 a d$

$v_f^2 - 0 = 2*9.8*57.8$

$v_f = 33.67 m/s$

Part c)

first rocket accelerate to reach height 26 meter and speed becomes 24.98 m/s

now we have

$v_f - v_i = a t$

$24.98 - 0 = 12*t_1$

$t_1 = 2.1 s$

after this it will reach to highest point and final speed becomes zero

$v_f - v_i = at$

$0 - 24.98 = -9.8 * t$

$t_2 = 2.55 s$

now from this it will fall back to ground and reach to final speed 33.67 m/s

now we have

$v_f - v_i = at$

$33.67 - 0 = 9.8 * t$

$t_3 = 3.44 s$

so total time is given as

<em>t = 3.44 + 2.55 + 2.1 = 8.1 s</em>

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3 years ago

At some instant and location the electric field associated with an electromagnetic wave in vacuum has the strength 96.5 V/m. Fin

prisoha [69]

Answer:

B = 32.17 x 10^-8 Tesla

u = 8.24 x 10^-8 J/m^3

P/A = 24.72 W/m^2

Explanation:

E = 96.5 V/m

velocity of light, c = 3 x 10^8 m/s

Let B be the magnetic field.

The relation between the electric field strength and the magnetic field strength is given by

B = E / c = 96.5 / (3 x 10^8) = 32.17 x 10^-8 Tesla

Let u be the energy density.

$u = \frac{1}{2}\times \varepsilon _{0}E^{2}+\frac{1}{2\mu _{0}}B^{2}$

$u = \frac{1}{2}\times 8.854\times 10^{-12}\times 96.5\times 96.5+\frac{1}{2\times 4\times 3.14\times 10^{-7}}\times 32.17^{2}\times 10^{-16}$

u = 8.24 x 10^-8 J/m^3

Let Power flow per unit area is

P/A = u x c = 8.24 x 10^-8 x 3 x 10^8 = 24.72 W/m^2

7 0

3 years ago

Anna35 [415]

Answer:

430.

Explanation:

If we know that 0.5 is half of a whole number, then we can simply understand that we need to 215 x 2 to get our answer.

3 0

3 years ago

Determine the electric field (in N/C) required to give the maximum possible deviation angle. (Enter the magnitude.)

Zigmanuir [339]

Answer:

Maximum angle = 3.43⁰

Explanation:

Say that you are given the following information:

vertical distance between the charge plate = 0.03 m

length of the plate = 0.5 m

velocity of the electrons = 5 × 10⁶ ms⁻¹

the maximum angle is given by the formula:

$tan\theta _{max} = \frac{d}{l}$

where d = vertical distance between the charge plate

l = length of the plate

substituting the values l and d gives:

$tan\theta _{max} = \frac{0.03}{0.5}$

maximum angle, $\theta _{max} = \frac{0.03}{0.5}$

$\theta _{max} = tan^{-1} (\frac{0.03}{0.5} )$

= 3.43⁰

3 0

3 years ago

To withstand ‘g-forces’ of up to 10 g’s, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a ‘human ce

Marina86 [1]

Answer:

34.292 m/s

Explanation:

When plane dives the gravitational acceleration becomes 10 times extra i-e

acceleration a = g= 10g's=10 ×9.8= 98 m/sec2

radius of dive circle = 12 m

v= speed= ?

Using

$a= \frac{v^{2} }{r}$

==> $v^{2}$ = a × r = 98 × 12 = 1176 $(\frac{m}{s}) ^{2}$

==> v= $\sqrt{1176(\frac{m}{s} )^{2} }$

==> v= 34.292 m/s

4 0

3 years ago