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tiny-mole [99]
3 years ago
13

A single conservative force acts on a 5.30-kg particle within a system due to its interaction with the rest of the system. The e

quation
Fx = 2x + 4
describes the force, where Fx is in newtons and x is in meters. As the particle moves along the x axis from x = 1.08 m to x = 6.50 m, calculate the following.
(a) the work done by this force on the particle
1 J
(b) the change in the potential energy of the system
2 J
(c) the kinetic energy the particle has at x = 6.50 m if its speed is 3.00 m/s at x = 1.08 m
3 J
Physics
1 answer:
cupoosta [38]3 years ago
8 0

Answer:

Given that

m = 5.3 kg

Fx = 2x + 4

We know that work done by force F given as

w= ∫ F. dx

a)

Given that x=1.08 m to x=6.5 m

Fx = 2x + 4

w= ∫ F. dx

w=\int_{1.08}^{6.5}(2x+4) .dx

w=\left [x^2+4x \right ]_{1.08}^{6.5}

w=(6.5^2-1.08^2)+4(6.5-1.08)\ J

w=62.7 J

b)

We know that potential energy given as

F=-\dfrac{dU}{dx}

∫ dU =  -∫F.dx           ( w= ∫ F. dx)

ΔU= -62.7 J

c)

We know that form work power energy theorem

Net work = Change in kinetic energy

W= KE₂ - KE₁

62.7 =KE₂ - (1/2)x 5.3 x 3²

KE₂ = 86.55 J

This is the kinetic energy at 6.5m

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baherus [9]

\huge\underline\mathtt\colorbox{cyan}{G=}

6.673 \times  {10}^{ - 11}

And unit is Nm^2/kg^2

8 0
2 years ago
Read 2 more answers
A centrifuge used in DNA extraction spins at a maximum rate of 7000rpm producing a "g-force" on the sample that is 6000 times th
defon

Answer:

A) a = 73.304 rad/s²

B) Δθ = 3665.2 rad

Explanation:

A) From Newton's first equation of motion, we can say that;

a = (ω - ω_o)/t. We are given that the centrifuge spins at a maximum rate of 7000rpm.

Let's convert to rad/s = 7000 × 2π/60 = 733.04 rad/s

Thus change in angular velocity = (ω - ω_o) = 733.04 - 0 = 733.04 rad/s

We are given; t = 10 s

Thus;

a = 733.04/10

a = 73.304 rad/s²

B) From Newton's third equation of motion, we can say that;

ω² = ω_o² + 2aΔθ

Where Δθ is angular displacement

Making Δθ the subject;

Δθ = (ω² - ω_o²)/2a

At this point, ω = 0 rad/s while ω_o = 733.04 rad/s

Thus;

Δθ = (0² - 733.04²)/(2 × 73.304)

Δθ = -537347.6416/146.608

Δθ = - 3665.2 rad

We will take the absolute value.

Thus, Δθ = 3665.2 rad

8 0
3 years ago
A 71 kW radio station broadcasts its signal uniformly in all directions. - What is the average intensity of its signal at a dist
marshall27 [118]

Answer:

Explanation:

Energy of signal being radiated per second on all sides = 71 x 10³ J .

At a distance of 220 m it is spread over an area of 4 π x (220)² because it is spreading uniformly on all sides.

So energy crossing per unit area

= \frac{71\times10^3}{4 \times \pi\times(220)^2}

= 11.67 x 10⁻² Wm⁻²s⁻¹.

This is the intensity of the signal.

At 2200 m this intensity will further reduce by 100 times

So there it becomes equal to

11.67 x 10⁻⁴ Wm⁻² s⁻¹.

3 0
3 years ago
How much heat is lost by 2.0 grams of water if the temperature drops from 31 °C to 29 °C? The specific heat of water is 4.184 J/
Elanso [62]

Given :

Mass of water, m = 2 grams.

The temperature of water drops from 31 °C to 29 °C .

The specific heat of water is 4.184 J/(g • °C).

To Find :

Amount of heat lost in this process.

Solution :

We know, heat lost is given by :

Heat\ lost,H = ms( T_f - T_i)\\\\H = 2\times 4.184 \times ( 31 - 29 )\ J\\\\H = 16.736\ J

Therefore, amount of heat lost in this process is 16.736 J.

4 0
3 years ago
What is the density of this liquid that has a mass of 300g and volume 600ml.
8_murik_8 [283]

Answer:

0.5

Explanation:

D = M / V

You divide 300g by 600ml and you get 0.5

(✿◠‿◠)

8 0
3 years ago
Read 2 more answers
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