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3 years ago

12

Two uniform solid spheres, A and B have the same mass. The radius of sphere B is twice that of sphere A. The axis of rotation pa

sses through the center of each sphere. Which one of the following statements concerning the moments of inertia of these spheres is true?

1 answer:

Svetach [21]3 years ago

4 0

Answer:

Sphere B has 4 times more inertia than sphere A.

Explanation:

Inertia on a Solid sphere is given by:

$I = 2/5*M*R^2$

For this problem:

ma = mb = M

Rb = 2*Ra

With these values:

$Ia = 2/5*M*Ra^2$

$Ib = 2/5*M*(2*Ra)^2 = 4* (2/5*M*Ra^2)$

As you can see, Ib = 4 * Ia.

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Energy may be measured in?

hram777 [196]

Answer:

Energy May be measured in joule

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3 years ago

Suppose you wish to whirl a pail full of water in a vertical circle at a constant speed without spilling any of its contents (ev

Yanka [14]

Answer:

V = 2.87 m/s

Explanation:

The minimum speed required would be that at which the acceleration due to gravity is negated by the centrifugal force on the water.

Thus, we simply need to set the centripetal acceleration equal to gravity and solve for the speed V using the following equation:

Centripetal acceleration = V^2 / r

where r is the distance of water from the pivot or shoulder.

For our case, r will be 0.65 + 0.19 = 0.84 m

and solving the above equation we get:

9.81 = V^2 / 0.84

V^2 = 8.2404

V = 2.87 m/s

6 0

3 years ago

A 3 kg object is moving along a horizontal surface. The kinetic energy of the object is increasing at a constant rate of 6 J/m;

Whitepunk [10]

To solve this problem we will apply the concepts of energy conservation and Newton's second law that defines force as the product of the object's mass with its acceleration. Additionally we will apply concepts related to the kinematics equations of linear motion.

For conservation of energy we have that work is equal to kinetic energy therefore,

$W = KE$

$Fd = \frac{1}{2} mv^2$

Here,

F = Force

d = Displacement

m = Mass

v= Velocity

At the same time we have the relation of

$F = \frac{W}{d}$

Therefore the value of the force can be interpreted as the rate of increase in energy per unit of distance, which makes it equivalent to

$F = \frac{W}{d} = 6J/m$

Applying Newton's Second Law

$F = ma$

$6J/m = (3kg)a$

$a = 2m/s^2$

In 4 seconds final velocity of the object becomes

$v = at$

$v= 2*4$

$v= 8m/s$

Then the work done is equal to,

$W = KE$

$W = \frac{1}{2} mv^2$

$W = \frac{1}{2} (3)(82)$

$W = 96J$

Then the displacement is,

$W = F*d$

$d = \frac{W}{F}$

$d = \frac{96}{6}$

$d = 16 m$

Therefore the distance moved is 16m

7 0

4 years ago

The speed of a particle moving in a circle 2.0 m in radius increases at the constant rate of 4.4 m/s2. At an instant when the ma

Law Incorporation [45]

Answer:

The speed of the particle is 2.86 m/s

Explanation:

Given;

radius of the circular path, r = 2.0 m

tangential acceleration, $a_t$ = 4.4 m/s²

total magnitude of the acceleration, a = 6.0 m/s²

Total acceleration is the vector sum of tangential acceleration and radial acceleration

$a = \sqrt{a_c^2 + a_t^2}\\\\$

where;

$a_c$ is the radial acceleration

$a = \sqrt{a_c^2 + a_t^2}\\\\a^2 = a_c^2 + a_t^2\\\\a_c^2 = a^2 -a_t^2\\\\a_c = \sqrt{a^2 -a_t^2}\\\\a_c = \sqrt{6.0^2 -4.4^2}\\\\a_c = \sqrt{16.64}\\\\a_c = 4.08 \ m/s^2$

The radial acceleration relates to speed of particle in the following equations;

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

where;

v is the speed of the particle

$v^2 = a_c r\\\\v= \sqrt{a_c r} \\\\v = \sqrt{4.08 *2}\\\\v = 2.86 \ m/s$

Therefore, the speed of the particle is 2.86 m/s

6 0

4 years ago

Which statement is true about the force of gravity?

kumpel [21]

Answer:

The moon's gravity pulls the Earth to make tides.

Explanation:

The Moons Gravity Pulls On The Earth With Different Strenght Making High Tide And Low Tide.

Hope This Helps!

4 0

3 years ago