As a planet's semimajor axis gets smaller, its speed will _______ and its period will ________

You obtain a 100-W light bulb and a 50-W light bulb. Instead of connecting them in the normal way, you devise a circuit that pla

lesantik [10]

Answer:

When they are connected in series

The 50 W bulb glow more than the 100 W bulb

Explanation:

From the question we are told that

The power rating of the first bulb is $P_1 = 100 \ W$

The power rating of the second bulb is $P_2 = 50 \ W$

Generally the power rating of the first bulb is mathematically represented as

$P_1 = V^2 R$

Where $V$ is the normal household voltage which is constant for both bulbs

So

$R_1 = \frac{V^2}{P_1 }$

substituting values

$R_1 = \frac{V^2}{100}$

Thus the resistance of the second bulb would be evaluated as

$R_2 = \frac{V^2}{50}$

From the above calculation we see that

$R_2 > R_1$

This power rating of the first bulb can also be represented mathematically as

$P_ 1 = I^2_1 R_1$

This power rating of the first bulb can also be represented mathematically as

$P_ 2 = I^2_2 R_2$

Now given that they are connected in series which implies that the same current flow through them so

$I_1^2 = I_2^2$

This means that

$P \ \alpha \ R$

So when they are connected in series

$P_2 > P_1$

This means that the 50 W bulb glows more than the 100 \ W bulb

3 0

4 years ago

In an experiment, a variable, position-dependent force F(x)F(x) is exerted on a block of mass 1.0kg1.0kg that is moving on a hor

leonid [27]

Answer:

The function F(x) for 0 < x < 5, the block's initial velocity, and the value of F(f).

(C) is correct option.

Explanation:

Given that,

Mass of block = 1.0 kg

Dependent force = F(x)

Frictional force = F(f)

Suppose, the following information would students need to test the hypothesis,

(A) The function F(x) for 0 < x < 5 and the value of F(f).

(B) The function a(t) for the time interval of travel and the value of F(f).

(C) The function F(x) for 0 < x < 5, the block's initial velocity, and the value of F(f).

(D) The function a(t) for the time interval of travel, the time it takes the block to move 5 m, and the value of F(f).

(E) The block's initial velocity, the time it takes the block to move 5 m, and the value of F(f).

We know that,

The work done by a force is given by,

$W=\int_{x_{0}}^{x_{f}}{F(x)\ dx}$ .....(I)

Where, $F(x)$ = net force

We know, the net force is the sum of forces.

So, $\sum{F}=ma$

According to question,

We have two forces F(x) and F(f)

So, the sum of these forces are

$F(x)+(-F(f))=ma$

Here, frictional force is negative because F(f) acts against the F(x)

Now put the value in equation (I)

$W=\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}$

We need to find the value of $\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}$

Using newton's second law

$\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}=\int_{x_{0}}^{x_{f}}{ma\ dx}$ ...(II)

We know that,

Acceleration is rate of change of velocity.

$a=\dfrac{dv}{dt}$

Put the value of a in equation (II)

$\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}=\int_{x_{0}}^{x_{f}}{m\dfrac{dv}{dt}dx}$

$\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}=\int_{v_{0}}^{v_{f}}{mv\ dv}$

$\int_{x_{0}}^{x_{f}}{(F(x)-F(f))dx}=\dfrac{mv_{f}^2}{2}+\dfrac{mv_{0}^2}{2}$

Now, the work done by the net force on the block is,

$W=\dfrac{mv_{f}^2}{2}+\dfrac{mv_{0}^2}{2}$

The work done by the net force on the block is equal to the change in kinetic energy of the block.

Hence, The function F(x) for 0 < x < 5, the block's initial velocity, and the value of F(f).

(C) is correct option.

7 0

3 years ago

A horizontal force in used to pull a 5 kilogram cart at a constant speed of 5 meters per second across the floor as shown in the

ddd [48]

A cart is pulled by horizontal force such that it moves with constant velocity

So here since velocity is constant we can say that its acceleration will be ZERO

now here for zero acceleration we can say

$F_{net} = 0$

So here we will have

$F_{net} = F_{ap} - F_f = 0$

here we know that

$F_f = 10 N$

so we will have

$F_{ap} - 10 = 0$

$F_{ap} = 10 N$

so here applied force on handle will be

5 0

3 years ago

Describe the three times acceleration can happen

Elden [556K]

Answer:

There are three ways an object can accelerate: a change in velocity, a change in direction, or a change in both velocity and direction.

Explanation:

7 0

3 years ago

Read 2 more answers

A traveling sinusoidal electromagnetic wave in vacuum has an electric field amplitude of 96.9 V/m. Find the intensity of this wa

lukranit [14]

Answer:

the intensity of this wave, I = 12.42 W/m²

the energy of this wave, U = 4.2 J

Explanation:

Given;

peak electric field, E₀ = 96.9 V/m

time of flow, t = 14.9s

area through which the energy flows, A = 0.0227 m²

The intensity of this wave is calculated using the following formula;

$I = \frac{E_{rms}^2}{c \mu_o}$

where;

root-mean-square electric field, $E_{rms} = \frac{E_o}{\sqrt{2}} = \frac{96.9}{\sqrt{2} } = 68.5187 \ V/m$

c is speed of light, c = 3 x 10⁸ m/s

μ₀ is permeability of free space (constant), μ₀ = 1.26 x 10⁻⁶

Substitute these values and calculate the intensity of the wave;

$I = \frac{E_{rms}^2}{c \mu_o} = \frac{(68.5187)^2}{(3*10^8)(1.26*10^{-6})} = 12.42 \ W/m^2$

Thus, intensity of this wave is 12.42 W/m²

The energy of the wave is calculated as follows;

U = IAt

U = 12.42 x 0.0227 x 14.9

U = 4.2 J

Thus, the energy of this wave is 4.2 J

6 0

4 years ago

As a planet's semimajor axis gets smaller, its speed will _______ and its period will _________ .

As a planet's semimajor axis gets smaller, its speed will _ and its period will ___ .