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3 years ago

Two books with different masses fall off the same bookshelf. As they fall,which has more kinetic energy and why

1 answer:

Alex3 years ago

5 0

Kinetic energy E = m * v^2

<span>Since the acceleration of both books will be -neglecting air resistance - the same, the kinetic energy will be directly proportional to the mass of the book.</span>

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Fan object moves in uniform circular motion in a circle of radius R=200 meters, and the objectes 5.00 seconds to

Leviafan [203]

Answer:

The centripetal acceleration of the object is $31550.72\ m/s^2$ .

Explanation:

We have,

Radius of a circular path is 200 m

It takes 5 seconds to complete 10 revolutions. The angular velocity of the object is given by the rate of change of angular displacement per unit time :

$\omega=\dfrac{\Delta \theta}{\Delta t}\\\\\omega=\dfrac{2\pi \times 10}{5}\\\\\omega=12.56\ rad/s$

The centripetal acceleration of the object is given by :

$a=\omega^2 r\\\\a=(12.56)^2 \times 200\\\\a=31550.72\ m/s^2$

So, the centripetal acceleration of the object is $31550.72\ m/s^2$ .

6 0

2 years ago

In a hydroelectric power plant, 65 m3 /s of water flows from an elevation of 90-m to a turbine-generator, where electricity is g

Mariulka [41]

The electric output of the plant is 48.19 MW

First we need to calculate the water power, it is given by the formula

WP=ρQgh

Here, ρ=1000 kg/m3 is density of water,Q is the flow rate, g is the gravity, and h is the water head

Therefore, WP=1000*65*9.81*90=57388500 W=57.38 MW

Now the overall efficiency of the hydroelectric power plant is given as

η= $\frac{electric power}{water power}$

Plugging the values in the above equation

0.84=EP/57.38

EP=48.19 MW

Therefore, the electric output of the plant is 48.19 MW.

3 0

2 years ago

3- (a) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given that Earth has a

ASHA 777 [7]

Explanation:

a) The Earth makes 1 rotation in 24 hours. In seconds:

24 hr × (3600 s / hr) = 86400 s

b) 1 rotation is 2π radians. So the angular velocity is:

2π rad / 86400 s = 7.27×10⁻⁵ rad/s

c) The earth's linear velocity is the angular velocity times the radius:

40075 km × 7.27×10⁻⁵ rad/s = 2.91 km/s

7 0

3 years ago

What is the equation describing the motion of a mass on the end of a spring which is stretched 8.8 cm from equilibrium and then

Sedbober [7]

Answer:

$x=(0.088m)\cos(\sqrt{\frac{k}{m} } t)$

Explanation:

We first identify the elements of this simple harmonic motion:

The amplitude A is 8.8cm, because it's the maximum distance the mass can go away from the equilibrium point. In meters, it is equivalent to 0.088m.

The angular frequency ω can be calculated with the formula:

$\omega =\sqrt{\frac{k}{m}}$

Where k is the spring constant and m is the mass of the particle.

Now, since the spring starts stretched at its maximum, the appropriate function to use is the positive cosine in the equation of simple harmonic motion:

$x=A\cos(\omega t)$

Finally, the equation of the motion of the system is:

$x=(0.088m)\cos(\omega t)$

$x=(0.088m)\cos(\sqrt{\frac{k}{m} } t)$

7 0

3 years ago

To lift a load of 100 kg a distance of 1 m an effort of 25 kg must be applied over an inclined plane of length 4 m. What must be

Troyanec [42]

Using conservation of energy law:-
∑ work in = ∑ work out
and work= force* displacement
so when we wanted to move a 100kg a distance of 1m
we multiplied 100*1 = work out
so work in should be equal to 100*g Joules, where g is the acceleration due to gravity.
so workout = 100*g = 25*g *x (divide both sides by 25*g)
x=4m

by the same way:-
------------------------
work in = 100kg * 2m * g (m/ $s^2$ )= work out
so work out = 25*x*g = 200* g (divide both sides by 25*g)
x=8m

6 0

2 years ago

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