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3 years ago

15

A light spring stretches 0.13 m when a 0.35 kg mass is hung from it. The mass is pulled down from this equilibrium position an a

dditional 0.15 m and then released. Determine the maximum speed of the mass.

1 answer:

Alenkasestr [34]3 years ago

6 0

Answer:

v = 1.30 m/s

Explanation:

given,

mass hung = 0.35 Kg

spring stretched when load is hanged (x)= 0.13 m

now,

weight of the mass attached = Kx

m g = k x

0.35 x 9.8 = k x 0.13

k = 26.38 N/m

now, using conservation of energy

$\dfrac{1}{2}mv^2 = \dfrac{1}{2}kx'^2$

$v = \sqrt{\dfrac{kx'^2}{m}}$

$v = \sqrt{\dfrac{26.38 \times 0.15^2}{0.35}}$

$v = \sqrt{1.6958}$

v = 1.30 m/s

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A red train travelling at 72 km/h and a green train travelling at 144 km/h are headed toward each

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Answer:

Collision will occur.

Speed of red train when they collide = 0 m/s.

Speed of green train when they collide = 10 m/s.

Explanation:

Speed of red train = 72 km/h = 20 m/s

Speed of green train = 144 km/h = 40 m/s.

Deceleration of trains = 1 m/s²

For red train:-

Equation of motion v = u + at

u = 20 m/s

v = 0 m/s

a = -1 m/s²

Substituting

0 = 20 - 1 x t

t = 20 s.

Equation of motion s = ut + 0.5at²

u = 20 m/s

t = 20 s

a = -1 m/s²

Substituting

s = 20 x 20 - 0.5 x 1 x 20² = 200 m

So red train travel 200 m before coming to stop.

For green train:-

Equation of motion v = u + at

u = 40 m/s

v = 0 m/s

a = -1 m/s²

Substituting

0 = 40 - 1 x t

t = 40 s.

Equation of motion s = ut + 0.5at²

u = 40 m/s

t = 40 s

a = -1 m/s²

Substituting

s = 40 x 40 - 0.5 x 1 x 40² = 800 m

So green train travel 800 m before coming to stop.

Total distance traveled = 800 + 200 = 1000 m>950 m.

So both trains collide.

Distance traveled by green train when red train stops(t=20s)

Equation of motion s = ut + 0.5at²

u = 40 m/s

t = 20 s

a = -1 m/s²

Substituting

s = 40 x 20 - 0.5 x 1 x 20² = 600 m

Total distance after 20 s = 600 + 200 = 800 m< 950m . So they collide after red train stops.

Speed of red train when they collide = 0 m/s.

Distance traveled by green train when they collide = 950 - 200 = 750 m

Equation of motion v² = u² + 2as

u = 40 m/s

s= 750 m

a = -1 m/s²

Substituting

v² = 40² - 2 x 1 x 750 = 100

v = 10 m/s

Speed of green train when they collide = 10 m/s.

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3 years ago

Suppose that the inverse market demand for silicone replacement tips for Sony earbud headphones is p = pN - 0.1Q, where p is t

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Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The effect of a change in the price of a new pair of headphones on the equilibrium price of replacement tips ( dp/dpN) is

$\frac{\delta p}{\delta p_N} =1$

b

The value of Q and p at equilibruim is

$Q_e = 250$ and $p_d =$ 5

The consumer surplus is $C= 3125$

The producer surplus is $P = 375$

Explanation:

From the question we are told that

The inverse market demand is $p_d = p_N -0.1Q$

The inverse supply function is $p_s = 2+ 0.012Q$

a

The effect of change in the price is mathematically given as

$\frac{\delta p}{\delta p_N}$

Now differntiating the inverse market demand function with respect to $p_N$

We get that

$\frac{\delta p}{\delta p_N} =1$

b

We are told that $p_N =$ $30

Therefore the inverse market demand becomes

$p_d = 30 -0.1Q$

At equilibrium

$p_d = p_s$

So we have

$30 -0.1Q_e = 2+ 0.012Q_e$

Where $Q_e$ is the quantity at equilibrium

$28 = 0.112Q_e$

$Q_e = \frac{28}{0.112}$

$Q_e = 250$

Substituting the value of Q into the equation for the inverse market demand function

$p_d = 30 - 0.1 (250 )$

$p_d =$ 5

Looking at the equation for $p_d \ and \ p_s$ we see that

For Q = 0

$p_d = 30$

$p_s =2$

And for Q = 250

$p_d = 5$

$p_s = 5$

Hence the consumer surplus is mathematically evaluated as

$C = \frac{1}{2} * Q_e * (30 -5)$

Substituting value

$C = \frac{1}{2} * 250 (30-5)$

$C= 3125$

And

The producer surplus is mathematically evaluated as

$P = \frac{1}{2} *250 * (5-2)$

$P = 375$

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How do physicists use measurements to understand the natural world?? Use scientific language to describe your evidence.

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Answer:

Measurements are used to describe quantitatively real-life situations

Explanation:

Measurement refers to the act of assigning a number (with a unit) to a characteristic of an object or an event.

For example: when we want to measure the size of an object, we can use a rule to measure its length, and we assign a number with a unit for that quantity (for example, 5 cm). In this case, we have done a measurement.

Measurements are used by scientists in order to understand the natural worlds. In fact, without measurements it would be impossible to describe phenomena of the real world quantitatively: it would be only possible to describe them qualitatively, and therefore it would not be possible for instance to derive mathematical laws that describe those phenomena.

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An internal combustion engine uses fuel, of energy content 44.4 MJ/kg, at a rate of 5 kg/h. If the efficiency is 28%, determine

Alika [10]

Efficiency = Power Output / Power Input

Power Input = Rate of Energy input = 44.4 MJ/kg * 5 kg/h

= 222 MJ/h

But 1 hour = 3600seconds

222 MJ/h = 222 MJ/3600s = 0.061667 MW J/s = Watts

Power input = 0.061667 MW = 61 667 W

From Efficiency = Power Output / Power Input

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