All categories

3 years ago

Which of these equations is dimensionally correct?

Physics

1 answer:

8_murik_8 [283]3 years ago

3 0

Answer: first and third.

Explanation:

An equation is dimensionally correct if the units are the same in both sides of the equation.

first, let's define the units used:

{m} = kg

{v} = m/s

{F} = kg*m/s^2

{x} = m

{t} = s

{a} = m/s^2

Now, let's analyze each option:

1) m*v/t = F

in the left side the units are:

{m}*{v}/{t} = kg*(m/s)*(1/s) = kg*m/s^2

And as is written above, these are the units of F, so this is correct.

2) x*v^2 = F*(x^3/x^2)

This is more trivial, in the right side we can see an F, that has mass units (kg) and in the left side we have x and v, and we know that none of these have mass units, so this expression is not correct.

3) xt= vt^2+at^3

the units in the right side are:

{x}*{t] = m*s

in the right side are:

{v}*{t}^2 + {a}*{t}^2 = (m/s)*s^2 + (m/s^2)*s^3 = m*s + m*s

So in both sides of the equation we have the same units, then this equation is dimensionally correct.

You might be interested in

2. A rock is dropped off a bridge. How fast is the rock

zhenek [66]

Answer:

a) The velocity of rock at 1 second, v = 9.8 m/s

b) The velocity of rock at 3 second, v = 29.4 m/s

c) The velocity of rock at 5.5 second, v = 53.9 m/s

Explanation:

Given data,

The rock is dropped from a bridge.

The initial velocity of the rock, u = 0

a) The velocity of rock at 1 second,

Using the first equation of motion

v = u + gt

v = 0 + 9.8 x 1

v = 9.8 m/s

b) The velocity of rock at 3 second,

v = u + gt

v = 0 + 9.8 x 3

v = 29.4 m/s

c) The velocity of rock at 5.5 second,

v = u + gt

v = 0 + 9.8 x 5.5

v = 53.9 m/s

5 0

4 years ago

fomenos

Answer:

The bulbs should be connected in parallel.

Explanation:

We want to find out a way to hook up 2 light bulbs and a battery so that when one bulb burns out or is disconnected the other bulbs stays lit.

We must connect the two bulbs in parallel so that even when one bulb is burns out, it will have no effect on the other bulb and the 2nd bulb will keep on working. The current flowing in each bulb will depend upon the resistance of each bulb and the voltage will be same across each bulb.

On the other hand, if we use a series circuit then if one bulb burns out then the there is no flow of current in the circuit and therefore, the second bulb will not be operational.

The current flowing through each bulb is given by

I = V/R

The voltage across each bulb is given by

V = IReq

Where I is the current and Req is the equivalent resistance of the two bulbs connected in parallel and is given by

Req = (R₁*R₂)/(R₁+R₂)

The connection diagram is attached where two bulbs are connected in parallel and are power with a battery.

4 0

3 years ago

A coyote can locate a sound source with good accuracy by comparing the arrival times of a sound wave at its two ears. Suppose a

jeka94

Answer:

a) t_l - t_r = 12.54 us

b) (t_l - t_r) / T = 0.0157

Explanation:

Given:

- Frequency of source f = 1250 Hz

- Distance from source to right ear d_r = 2.6 m

- Distance from source to left ear d_l = ?

- Separation between ears s = 0.15 m

Find:

a. What is the difference in the arrival time of the sound at the left ear and the right ear?

b. What is the ratio of this time difference to the period of the sound wave?

Solution:

- Apply Pythagoras theorem to calculate the distance d_l from source to left ear:

d_l = sqrt ( 2.6^2 + 0.15^2)

d_l = sqrt ( 6.7825 )

d_l = 2.6043 m

- The time deference can be calculated from a simple distance - speed formula:

t_l - t_r = (1 / v) * ( d_l - d_r)

Where, v = 343 m/s speed of sound in air:

t_l - t_r = (1 / 343) * ( 2.6043 - 2.6)

t_l - t_r = ( 0.0043 / 343 )

t_l - t_r = 12.54 us

- Now we compute the Time period of the sound wave:

T = 1 / f

T = 1 / 1250 = 8*10^-4 s

- The ratio of differential time to Time period T is:

(t_l - t_r) / T = 12.54 * 10^-6 / 8*10^-4

(t_l - t_r) / T = 0.0157

3 0

3 years ago

What are the results of habitat loss? choose the most likely outcome

zmey [24]

The Answer that makes the most sense is C.

5 0

3 years ago

Read 2 more answers

Mike has a mass of 97 kg. He jumps out of a perfectly good airplane that is 2000 m above the ground. After he falls 1000 m, when

Ne4ueva [31]

Answer:

a) fr = 224.3 N , b) fr = 224.3 N , c) v = 198.0 m/s

Explanation:

a) For this exercise let's start by calculating the acceleration in the fall

v² = v₀² - 2 a (y-y₀)

When it jumps the initial vertical speed is zero

a = -v² / 2 (y-y₀)

a = -68 2/2 (1000-2000)

a = 2,312 m / s²

Let's use the second net law to enter the average friction force

fr = m a

fr = 97 2,312

fr = 224.3 N

b) let's look for acceleration

v² = v₀² - 2 a y

a = (v² –v₀²) / 2 (y-y₀)

a = (4² - 68²) / 2 (0-1000)

a = 2,304 m / s²

fr = m a

fr = 97 2,304

fr = 223.5 N

c) the speed of the wallet is searched with kinematics

v² = v₀² - 2 g (y-y₀)

v = √ (0-2 9.8 (0-2000))

v = 198.0 m/s

4 0

3 years ago