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bogdanovich [222]
1 year ago
5

A 40,000 kg subway train is brought to a stop from a speed of 0.700 m/s in 0.250 m by a large spring bumper at the end of its tr

ack. What is the force constant k of the spring?

Physics
1 answer:
lozanna [386]1 year ago
5 0

Given,

The mass of the train, m=40000 kg

The initial velocity of the train, u=0.700 m/s

The compression in the spring bumper that stopped the train, x=0.250 m

The final velocity of the train, v=0 m/s

From the equation of motion,

v^2-u^2=2ax

Where a is the acceleration of the train.

On substituting the known values,

\begin{gathered} 0-0.700^2=2a\times0.250 \\ \Rightarrow a=\frac{-0.700^2}{2\times0.25} \\ =-0.98\text{ m/s}^2 \end{gathered}

The magnitude of the force applied by the train will be equal to the magnitude of the restoring force of the spring.

Therefore,

\begin{gathered} m|a|=kx \\ \Rightarrow k=\frac{m|a|}{x} \end{gathered}

Where k is the spring constant of the spring.

On substituting the known values,

\begin{gathered} k=\frac{40000\times0.98}{0.250} \\ =156800\text{ N/m} \end{gathered}

Therefore the spring constant of the spring is 156800 N/m

Thus the correct answer is option C.

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strojnjashka [21]

Kinetic energy per unit of mass is

K=\frac{v^{2} }{2}

Given, v=3m/s^{2}

Therefore,

K=\frac{(3^{2} m/s^{2} )^2}{2}

K=4.5 J/kg

Now potential energy per unit mass is

p=g\times h

Given, h=90 m

Therefore,

p= 9.8m/s^2 \times 90

p=882.9 J/kg

Thus, total mechanical energy of the river water per unit mass is

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OR

T=0.887 kJ/kg

6 0
3 years ago
Sulfur hexafluoride is represented by which formula? A) sf2 b) sf7 c) s2f5 d) sf6
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You have a flag pole at an angle of 45 degrees to a wall it is designed to support a max torque of 40Nm. You bought a new one wi
In-s [12.5K]

Answer:

0.915 rad or 52.44 degrees

Explanation:

Let g = 10 m/s2. We can calculate the gravity force acting on center of mass of the new 8.75 kg pole:

F = mg = 8.75 * 10 = 87.5 kg

The moment is the dot product of force and moment arm

M = \vec{F} \cdot \vec{r} = Frcos\theta = 87.5*0.75cos\theta = 65.625cos\theta

where θ is the angle between the gravity force and the pole, or between the pole and the wall. As M can be at its max, which is 40 Nm, we can solve for θ:

62.625cos\theta = 40

cos\theta = 40 / 62.625 = 0.61

\theta = cos^{-1}0.61 = 0.915 rad = 0.915 * 180 /\pi = 52.44^o

7 0
3 years ago
Given the atomic radius of argon, 0.97 Å, and knowing that a sphere has a volume of 4πr3/3, calculate the fraction of space that
Bogdan [553]

Answer:

1.0x10^-4

Explanation:

First, in order to do this, we need to calculate the volume of 1 simple atom of Ar. Using the formula of the volume of a sphere we have the following

Converting A to cm:

0.97 * 1x10^-8 = 9.7x10^-9 cm

Now the volume:

V = 4/3π(9.7x10^-9)³

V = 3.82x10^-24 cm³

We know that 1 cm³ is 1 mL, and 1 L is 1000 mL so:

V = 3.82x10^-24 mL / 1000 = 3.82x10^-27 L

Now, using avogadro's number, we should get the total volume of all atoms of Ar so:

3.82x10^-27 * 6.02x10^23 = 2.3x10^-3 L

Finally, at STP the volume of an ideal gas is 22.4 L so:

2.3x10^-3 / 22.4 = 1.03x10^-4

With two significant figure, it would be 1.0x10^-4

5 0
2 years ago
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