Different colors of light correspond to different light

A mass MM uniform solid cylinder of radius RR and a mass MM thin uniform spherical shell of radius RR roll without slipping. If

vampirchik [111]

Answer:

vcyl / vsph = 1.05

Explanation:

The kinetic energy of a rolling object can be expressed as the sum of a translational kinetic energy plus a rotational kinetic energy.
The traslational part can be written as follows:

$K_{trans} = \frac{1}{2}* M* v_{cm} ^{2} (1)$

The rotational part can be expressed as follows:

$K_{rot} = \frac{1}{2}* I* \omega ^{2} (2)$

where I = moment of Inertia regarding the axis of rotation.
ω = angular speed of the rotating object.
If the object has a radius R, and it rolls without slipping, there is a fixed relationship between the linear and angular speed, as follows:

$v = \omega * R (3)$

For a solid cylinder, I = M*R²/2 (4)
Replacing (3) and (4) in (2), we get:

$K_{rot} = \frac{1}{2}* \frac{1}{2} M*R^{2} * \frac{v_{cmc} ^{2}}{R^{2}} = \frac{1}{4}* M* v_{cmc}^{2} (5)$

Adding (5) and (1), we get the total kinetic energy for the solid cylinder, as follows:

$K_{cyl} = \frac{1}{2}* M* v_{cmc} ^{2} +\frac{1}{4}* M* v_{cmc}^{2} = \frac{3}{4}* M* v_{cmc} ^{2} (6)$

Repeating the same steps for the spherical shell:

$I_{sph} = \frac{2}{3} * M* R^{2} (7)$

$K_{rot} = \frac{1}{2}* \frac{2}{3} M*R^{2} * \frac{v_{cms} ^{2}}{R^{2}} = \frac{1}{3}* M* v_{cms}^{2} (8)$

$K_{sph} = \frac{1}{2}* M* v_{cms} ^{2} +\frac{1}{3}* M* v_{cms}^{2} = \frac{5}{6}* M* v_{cms} ^{2} (9)$

Since we know that both masses are equal each other, we can simplify (6) and (9), cancelling both masses out.
And since we also know that both objects have the same kinetic energy, this means that (6) are (9) are equal each other.
Rearranging, and taking square roots on both sides, we get:

$\frac{v_{cmc}}{v_{cms}} =\sqrt{\frac{10}{9} } = 1.05 (10)$

This means that the solid cylinder is 5% faster than the spherical shell, which is due to the larger moment of inertia for the shell.

3 0

2 years ago

chris and molly wins $2400 in a competition they share the money in the ratio2:3 how much money do they each receive ?

nlexa [21]

Answer:

chris gets 960 and molly gets 1440

Explanation:

add the ratio up and divide

2+3=5

2400/5=480

480x2=960

480x3=1440

960+1440= 2400

5 0

3 years ago

A 1-kg block is lifted vertically 1 m at constant speed by a boy. The work done by the boy is about:

Igoryamba

Answer:

$9.8\; {\rm J}$ , assuming that the gravitational field strength is $g = 9.8\; {\rm N \cdot kg^{-1}}$ .

Explanation:

Notice that both the speed and the direction of motion of this block are constant. In other words, the velocity of this block is constant.

By Newton's Second Law, the net force on this block would be $0$ . External forces on this block should be balanced. Thus, the magnitude of the (downward) weight of this block should be equal to the magnitude of the (upward) force that the boy applies on this block.

Let $m$ denote the mass of this block. It is given that $m = 1\; {\rm kg}$ . The weight of this block would be:

$\begin{aligned}\text{weight} &= m\, g \\ &= 1\; {\rm kg} \times 9.8\; {\rm N \cdot kg^{-1}} \\ &= 9.8\; {\rm N}\end{aligned}$ .

Hence, the force that the boy applies on this block would be upward with a magnitude of $F = 9.8\; {\rm N}$ .

The mechanical work that a force did is equal to the product of:

the magnitude of the force, and
the displacement of the object in the direction of the force.

The displacement of this block (upward by $s = 1\; {\rm m}$ ) is in the same direction as the (upward) force that this boy had applied. Thus, the work that this boy had done would be the product of:

the magnitude of the force that this boy exerted, $F = 9.8\; {\rm N}$ , and
the displacement of this block in the direction, $s = 1\; {\rm m}$ .

$\begin{aligned}\text{work} &= F\, s \\ &= 9.8\; {\rm N} \times 1\; {\rm m} \\ &= 9.8\; {\rm J}\end{aligned}$ .

5 0

1 year ago

If the angle of incidence of a light source to a shiny surface is 30 degrees, what will the angle

Virty [35]

<h3>Answer: D) 30</h3>

Angle of incidence always equals angle of reflection. Think of a tennis ball being hit into a wall. The ball will bounce off at the same angle that it approached with. The angles mentioned are formed through the line called the "normal", which is the line perpendicular to the surface.

5 0

3 years ago

Read 2 more answers

Heat is transferred from molecules with more kinetic energy to molecules with _________kinetic energy.

Karolina [17]

Answer:

low

Explanation:

the higher the kinetic energy, the More the vibration of molecules, thus heat is more on the side with highly vibrating molecules

3 0

2 years ago