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3 years ago

Which energy transformation propels a marathon runner across the finish line ?

1 answer:

4 0

A. chemical energy to kinetic energy
B.heat energy to mechanical energy

C.mechanical energy to electrical energy

D.kinetic energy to gravitational potential energy

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You have a two-wheel trailer that you pull behind your ATV. Two children with a combined mass of 77.2 kg hop on board for a ride

lions [1.4K]

To solve this problem it is necessary to apply the kinematic equations of motion and Hook's law.

By Hook's law we know that force is defined as,

$F= kx$

Where,

k = spring constant

x = Displacement change

PART A) For the case of the spring constant we can use the above equation and clear k so that

$k= \frac{F}{x}$

$k = \frac{mg}{x}$

$k= \frac{77.2*9.8}{0.0637}$

$k = 11876.92N/m$

Therefore the spring constant for each one is 11876.92/2 = 5933.46N/m

PART B) In the case of speed we can obtain it through the period, which is given by

$T = \frac{2\pi}{\omega}$

Re-arrange to find \omega,

$\omega = \frac{2\pi}{T}$

$\omega = \frac{2\pi}{2.14}$

$\omega = 2.93rad/s$

Then through angular kinematic equations where angular velocity is given as a function of mass and spring constant we have to

$\omega^2 = \frac{k}{m}$

$m = \frac{k}{\omega^2}$

$m = \frac{ 11876.92}{2.93}$

$m = 4093.55Kg$

Therefore the mass of the trailer is 4093.55Kg

PART C) The frequency by definition is inversely to the period therefore

$f = \frac{1}{T}$

$f = \frac{1}{2.14}$

$f = 0.4672 Hz$

Therefore the frequency of the oscillation is 0.4672 Hz

PART D) The time it takes to make the route 10 times would be 10 times the period, that is

$t_T = 10*T$

$t_T = 10 *2.14s$

$t_T = 21.4s$

Therefore the total time it takes for the trailer to bounce up and down 10 times is 21.4s

5 0

4 years ago

If you were “shopping” for an economical launch vehicle to launch 66 satellites within a year into Low Earth Orbit, to form a co

dezoksy [38]

Cost of vehicle, cost per launch, capacity of each vehicle, re-usability, size of vehicle, etc

8 0

3 years ago

A man can lift a mass of 200kg onThe surface of the earth. what is the amount of mass he can lift on the surface of the moon?

Arlecino [84]

Answer:

1,211.1 kg.

Explanation:

the force of gravity is less on the moon than on earth, so if the man can lift 200kg on earth, he could lift a greater amount on the moon because there is less resistance from gravity.

To know the amount of mass he can lift on the moon, we first need to know the amount of weight that is equivalent to those 200kg here on earth. This because the weight of the object is equal to the force that must be applied to lift it, and that force is applied by the man and it will be the same here and on the moon.

We calculate weight using the formula:

$w=mg$

where $w$ is the weight of the object (the force with which the earth attracts the object) $m$ is the mass and g the acceleration of gravity.

$w=200g$

for earth the acceleration due to gravity is: $g=9.81m/s^2$

thus:

$w=(200kg)(9.81m/s^2)\\w=1962N$

now we use this value to calculate the mass he can lift on the moon, since for the moon $g=1.62m/s^2$ .

we use the same equation, w =mg substituting w = 1962N and $g=1.62m/s^2$ :

$w=mg\\\\1962N=m(1.62m/s^2)\\\\m=\frac{1962N}{1.62m/s^2}\\\\ m=1,211.1kg$

he can lift 1,211.1 kg.

You can also find the result using the approximate value of the acceleration of gravity on the moon as g/6, where g is the acceleration on earth.

8 0

4 years ago

The swinging pendulum has 10 joules of potential energy at its maximum height at points (1) and (5). If the mass of the pendulum

SVEN [57.7K]

The speed of the pendulum at point 3 is 1.4 m/s

Explanation:

We can solve this problem by using the law of conservation of energy. In fact, the mechanical energy of the pendulum (which is the sum of his potential energy + his kinetic energy) must be conserved. So we can write:

$U_1 +K_1 = U_3 + K_3$