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3 years ago

Why is the restoring force in Hooke's law a negative value?

2 answers:

Rudiy273 years ago

8 0

It's a negative value because the negative sign on the spring's force means the force exerted opposes the spring's displacement

Colt1911 [192]3 years ago

4 0

Explanation:

Hooke's law :

According to the Hooke's law, The force is the directly proportional to the displacement of the string.

On the other hand,

In a simple harmonic motion, The restoring force is directly proportional to the displacement and acts in the opposite direction to that of displacement.

The restoring force is defined as,

$F\propto -x$

$F = -kx$

Where,

F = restoring force

k = restoring constant

x = displacement

The negative sign shows the force opposes the string's displacement

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The temperature of air changes from 0 to 10°C while its velocity changes from zero to a final velocity, and its elevation change

aliya0001 [1]

Answer:

Final velocity = 119.83 m/s

Final elevation = 731.9 m

Explanation:

We are told that temperature of air changes from 0 to 10°C

Thus;

Change in temperature; ΔT = 10 - 0 = 10°C

Also, its velocity changes from zero to a final velocity. Thus;

v1 = 0 m/s

v2 is unknown

Also, its elevation changes from zero to a final elevation.

So, z1 = 0 and z2 is unknown

Now, we want to find v2 and z2 when the internal, kinetic and potential energy are equal.

Thus Equating the formula for both kinetic and internal energy gives;

½m(v2² - v1²) = mc_v•ΔT

m will cancel out and v1 is zero to give;

v2² = 2c_v•ΔT

v2 = √(2c_v•ΔT)

Where c_v is specific heat of constant volume of air with a constant value of 718 J/Kg.K

Thus;

v2 = √(2 × 718 × 10)

v2 = √14360

v2 = 119.83 m/s

To find z2, we will equate potential energy formula to that of the internal energy.

Thus;

mg(z2 - z1) = mc_v•ΔT

m will cancel out and since z1 is zero, then we have;

z2 = (c_v•ΔT)/g

z2 = 718 × 10/9.81

z2 = 731.9 m

4 0

4 years ago

A cellist tunes the C string of her instrument to a fundamental frequency of 65.4 Hz. The vibrating portion of the string is 0.5

Dahasolnce [82]

Answer:

$\lambda = 1.18 \ m$

$v = 77.172 \ m/s$

$T = 151.41 \ N$

Explanation:

From the question we are told that

The frequency is $f = 65.4 \ Hz$

The length of the vibrating string is $L = 0.590 \ m$

The mass is $m = 15.0 \ g = 0.015 \ kg$

Generally the wavelength is mathematically represented as

$\lambda = 2 * L$

=> $\lambda = 2 * 0.590$

=> $\lambda = 1.18 \ m$

Generally the wave speed is

$v = \lambda * f$

=> $v = 1.18 * 65.4$

=> $v = 77.172 \ m/s$

Generally the tension on the wire is mathematically represented as

$T = v^2 * \frac{ m }{L }$

=> $T = 77.172 ^2 * \frac{ 0.015 }{0.590}$

=> $T = 151.41 \ N$

7 0

3 years ago

What does a curved gradient line in a distance-time graph represent?

GREYUIT [131]

Answer:

If the line is curved, the slope is changing, which also means the velocity is changing. In a distance-time graph, the gradient of the line is equal to the speed of the object. The more the gradient (and the steeper the line) the faster the object is moving.

4 0

3 years ago

A small airplane flies 780 miles with an average speed of 260 miles per hour. 1.5 hours after the plane leaves, a Boeing 747 lea

Lera25 [3.4K]

Answer:

520 miles per hour

Explanation:

Let the speed of the Boeing 747 be x miles per hour.

The small airplane covers distance of 780 miles with speed 260 miles per hour.

Also,

After 1.5 hours the Boeing 747 leave the same place and reaches at same time. Both covered distance of 780 miles.

So,

<u>Time taken by Boeing 747 + 1.5 hours = Time taken by small plane.</u>

Also,

Time = Distance/ speed

So,

780 / x + 1.5 = 780/ 260

Solving for x, we get:

<u>x = 520 miles per hour</u>

6 0

4 years ago

What’s is the relationship between energy and motion ?

LekaFEV [45]

Motion energy is the sum of potential and kinetic energy in an object that is used to do work.

5 0

3 years ago