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3 years ago

If the merry-go-round makes one revolution in 10 seconds, what is the child’s linear speed?

1 answer:

5 0

The child's linear speed is

<em> (pi / 5) x (the child's distance from the center of the ride, in feet)</em>

feet per second.

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When two resistors are wired in series with a 12 V battery, the current through the battery is 0.33 A. When they are wired in pa

MA_775_DIABLO [31]

Answer:

If R₂=25.78 ohm, then R₁=10.58 ohm

If R₂=10.57 then R₁=25.79 ohm

Explanation:

R₁ = Resistance of first resistor

R₂ = Resistance of second resistor

V = Voltage of battery = 12 V

I = Current = 0.33 A (series)

I = Current = 1.6 A (parallel)

In series

$\text{Equivalent resistance}=R_{eq}=R_1+R_2\\\text {From Ohm's law}\\V=IR_{eq}\\\Rightarrow R_{eq}=\frac{12}{0.33}\\\Rightarrow R_1+R_2=36.36\\ Also\ R_1=36.36-R_2$

In parallel

$\text{Equivalent resistance}=\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\\\Rightarrow {R_{eq}=\frac{R_1R_2}{R_1+R_2}$

$\text {From Ohm's law}\\V=IR_{eq}\\\Rightarrow R_{eq}=\frac{12}{1.6}\\\Rightarrow \frac{R_1R_2}{R_1+R_2}=7.5\\\Rightarrow \frac{R_1R_2}{36.36}=7.5\\\Rightarrow R_1R_2=272.72\\\Rightarrow(36.36-R_2)R_2=272.72\\\Rightarrow R_2^2-36.36R_2+272.72=0$

Solving the above quadratic equation

$\Rightarrow R_2=\frac{36.36\pm \sqrt{36.36^2-4\times 272.72}}{2}$

$\Rightarrow R_2=25.78\ or\ 10.57\\ If\ R_2=25.78\ then\ R_1=36.36-25.78=10.58\ \Omega\\ If\ R_2=10.57\ then\ R_1=36.36-10.57=25.79\Omega$

∴ If R₂=25.78 ohm, then R₁=10.58 ohm

If R₂=10.57 then R₁=25.79 ohm

6 0

3 years ago

Which is true concerning the acceleration due to gravity? A. It decreases with increasing altitude. B. It is different for diffe

Kisachek [45]

Answer:

The correct answer is option 'a': It decreases with increase in altitude

Explanation:

Acceleration due to gravity is the acceleration that a body is subjected to when it is freely dropped from a height from surface of any planet, ignoring the resistance that the object may face in it's motion such as drag due to any fluid.. The acceleration due to gravity is same for all the objects and is independent of their masses, it only depends on the mass of the planet and the radius of the planet on which the object is dropped. it's values varies with:

1) Depth from surface of planet.

2)Height from surface of planet.

3) Latitude of the object.

Hence it neither is a fundamental quantity nor an universal constant.

The variation of acceleration due to gravity with height can be mathematically written as:

$g(h)=g_{surface}(1-\frac{2h}{R_{planet}})$

where,

R is the radius of the planet

$g_{surface}$ is value of acceleration due to gravity at surface.

hence we can see that upon increase in altitude the value of 'g' goes on decreasing.

5 0

3 years ago

What force is needed to accelerate a child on a sled at 1.25 m/s² is the total mass of the child and sled is 60 kg?

OverLord2011 [107]

Newton's 2nd law of motion: (Honestly, if you don't
remember this by now, you're going to have problems.)

Force = (mass) x (acceleration).

= (60 kg) x (1.25 m/s²)

= 90 kg-m/s²

= 90 Newtons .

5 0

3 years ago

Starting from rest near the surface of the Earth, a 25-kg beam slides 12 m down a vertical pine tree, and has a speed of 6 m/s j

Mamont248 [21]

Answer:

The frictional force acting on the bear during the slide is 207.5 N

Explanation:

Given;

mass of beam, m = 25-kg

vertical height, h = 12 m

speed of fall, v = 6 m/s

Change in potential energy of the beam: