Ask question

Ask question

All categories

1 year ago

11

The position of a particle moving along the x axis may be determined from the expression x(t) = btu + ctv, where x will be in me

ters when t is in seconds. What will be the dimensions of b and c in this case if u = 8 and v = 7?

1 answer:

KIM [24]1 year ago

8 0

As per given equation we have

$x = bt^u + ct^v$

now as per the dimensional analysis we can say that dimension of right side of equation must be equal to left side of the equation

now as per left side of equation its dimension is same as length or meter

now we can say it should be meter on right side also

$bt^u = M^0L^1T^0$

$b*T^8 = M^0L^1T^0$

$b = M^0L^1T^{-8}$

similarly for other term we have

$ct^v = M^0L^1T^0$

$c*T^7 = M^0L^1T^0$

$c = M^0L^1T^{-7}$

<em>so above are the dimensions of b and c</em>

You might be interested in

You discover a Cepheid variable star with a 30 day period in the Milky Way. Through careful monitoring for a few years with the

soldi70 [24.7K]

Answer:c

Explanation:

Bc it makes sense

3 0

2 years ago

A wind turbine with a rotor diameter of 40 m produces 90 kW of electrical power when the wind speed is 8 m/s. The density of air

aleksley [76]

Answer:

0.233

Explanation:

Given that

Diameter of rotor, d = 40 m

Power of rotor, P = 90 kW

Speed of the wind, v = 8 m/s

Density of air, p = 1.2 kg/m³

It is a known fact that

KE = ½mv², where mass flow rate, m

m = p.A.v, where Area, A

A = πd²/4

A = (3.142 * 40²)/4

A = 3.142 * 1600/4

A = 3.142 * 400

A = 1256.8 m², substitute for A in the mass flow rate equation

m = p.A.v

m = 1.2 * 1256.8 * 8

m = 12065.28, substitute for m in the KE equation

KE = ½mv²

KE = ½ * 12065.28 * 8²

KE = 12065.28 * 32

KE = 386088.96 W or

KE = 386.1 kW

Fraction of kinetic energy converted to electric energy is

Fraction = Electric Power / Total KE

Fraction = 90 / 386.1

Fraction = 0.233

8 0

2 years ago

A glider is gliding through the air at a height of 416 meters with a speed of 45.2 m/s. The glider dives to a height of 278 mete

Verdich [7]

Answer:

<em>The glider's new speed is 68.90 m/s</em>

Explanation:

<u>Principle Of Conservation Of Mechanical Energy</u>

The mechanical energy of a system is the sum of its kinetic and potential energy. When the only potential energy considered in the system is related to the height of an object, then it's called the gravitational potential energy. The kinetic energy of an object of mass m and speed v is

$\displaystyle K=\frac{1}{2}mv^2$

The gravitational potential energy when it's at a height h from the zero reference is

$U=mgh$

The total mechanical energy is

$M=K+U$

$\displaystyle M=\frac{1}{2}mv^2+mgh$

The principle of conservation of mechanical energy states the total energy is constant while no external force is applied to the system. One example of a non-conservative system happens when friction is considered since part of the energy is lost in its thermal manifestation.

The initial conditions of the problem state that our glider is glides at 416 meters with a speed of 45.2 m/s. The initial mechanical energy is

$\displaystyle M_1=\frac{1}{2}m(45.2)v_o^2+m(9.8)(416)$

Operating in terms of m

$\displaystyle M_1=1021.52m+4076.8m$

$\displaystyle M_1=5098.32m$

Then we know the glider dives to 278 meters and we need to know their final speed, let's call it $v_f$ . The final mechanical energy is

$\displaystyle M_2=\frac{1}{2}mv_f^2+m(9.8)(278)$

Operating and factoring

$\displaystyle M_2=m(\frac{1}{2}v_f^2+2724.4)$

Both mechanical energies must be the same, so

$\displaystyle m(\frac{1}{2}v_f^2+2724.4)=5098.32m$

Simplifying by m and rearranging

$\displaystyle \frac{v_f^2}{2}=5098.32-2724.4$

Computing

$v_f=\sqrt{4747.84}=68.90\ m/s$

The glider's new speed is 68.90 m/s

8 0

2 years ago

How long a time t will it take for the 133 54xe to decay so that eventually its activity decreases by a factor of 1024?

serg [7]

Base on my research the radioactive isotope X-133 has a half-life of 5 days. So base on the given it decreases by a factor of 1024, it represents 10 halvings. To get how long will it take for the 133 54xe to decay, just multiply 5 days with 10 halvings. The answer is 50 days for the 133 54xe to decay.

8 0

2 years ago

Read 2 more answers

To visit your favorite ice cream shop, you must travel 490 m west on Main Street and then 920 m south on Division Street. Suppos

topjm [15]

Answer:

a) The magnitude of your average velocity during the 121 s is 8.61 m/s.

b) The direction of the average velocity is 61.9° south of west.

c) Your average speed during the trip is 11.7 m/s

Explanation:

Hi there!

a) The average velocity (a.v) is calculated as the displacement divided by the time it took to do such a displacement.

The displacement is calculated as the distance between the initial position and the final position:

Displacement = Δ(x,y) = final position - initial position

Let's consider that your initial position is the origin of our frame of reference and let's also consider that west and south are positive directions (+x and +y respectively). Then the displacement vector will be:

Δ(x,y) = final positon - initial position

Δ(x,y) = (490, 920) m - (0, 0) m = (490, 920) m

The average velocity will be:

a.v = Δ(x,y) / t

a.v = (490, 920) m / 121 s

a.v = (4.05, 7.60) m/s

The magnitude of the average velocity is calculated as follows:

The magnitude of your average velocity during the 121 s is 8.61 m/s.

b) To find the direction of the average velocity, we have to use trigonometric rules of right triangles. Notice that the x and y-components of the average velocity (vx and vy) together with the average velocity vector (v), with magnitude 8.61 m/s, form a triangle (see figure).

Also, notice that v is the hypotenuse of the triangle and that vx is the side adjacent to the angle θ while vy is the side opposite to θ.

Using trigonometry, we can calculate the value of the angle θ:

cos θ = adjacent side / hypotenuse

cos θ = vx / v

cos θ = 4.05 m/s / 8.61 m/s

θ = 61.9°

The direction of the average velocity is 61.9° south of west.

c) The average speed (a.s) is calculated as the traveled distance (d) divided by the time it took to cover that distance (t). In total, you traveled (490 m + 920 m) 1410 m in 121 s, then the average speed will be:

a.s = d/t

a.s = 1410 m / 121 s

a.s = 11.7 m/s

Your average speed during the trip is 11.7 m/s

5 0

2 years ago