Ask question

Ask question

All categories

3 years ago

13

A child has two red wagons, with the rear one tied to the front by a (non-stretching) rope. If the child pushes on the rear wago

n, what happens to the kinetic energy of each of the wagons and the two-wagon system?

1 answer:

Sergeeva-Olga [200]3 years ago

5 0

Answer:

The rear wagon gains the kinetic energy, but the front wagon will remain at rest.

The two-wagon system will gain a kinetic energy $\dfrac{1}{16}$ of the kinetic energy gained by the rear wagon.

Explanation:

Let's consider that the masses of the wagons to be 'M'. When the child pushes the rear wagon let's assume that the velocity of the rear wagon be 'v'.

Therefor the kinetic energy gained by the rear wagon be $K_{r} = \frac{1}{2}Mv^{2}$ .

Now let's assume that the velocity of the centre of mass (C), as shown in the figure, be 'V'. So from momentum conservation law we can write,

$&& Mv = (M + M)V\\\\&or,& V = \frac{v}{2}$

Now the centre of mass ( $M_{C}$ ) is given by

$M_{C} = \frac{M \times M}{M + M} = \frac{M}{2}$

So the kinetic energy ( $K_{C}$ ) of the system will be

$K_{C} = \frac{1}{2}M_{C}V^{2} = \frac{1}{2}\frac{M}{2}(\frac{v}{2})^{2} = \frac{1}{16}Mv^{2}$

You might be interested in

An object goes from a speed of 9m/s to a total stop in 3 s. what is the object's acceleration

timama [110]

A = dv/dt = ak
ak = ( 0.0 m/s - 9.0 m/s ) / ( 3 s )

3m/s^2

3 0

3 years ago

When traveling on a two-lane highway driving 50 to 55 mph, you need a _____ gap in oncoming traffic to pass safely?

JulsSmile [24]

When travelling on a two lane highway driving 50 to 55 mph, you need a 10-12 second gap in oncoming traffic to pass safety. At 55 mph, you will travel over 800 feet in 10-12 seconds so will an oncoming vehicle. That means you need over 1600 feet which is about 1/3 of a mile to pass safety. It is harder to see and judge the speed of oncoming vehicles that are traveling 1/3 of a mile or more away from you.

3 0

4 years ago

A vertical piston cylinder device is being used to heat water. the piston has a mass of 20 kg and a cross sectional area of 100

Leni [432]

A boiling pot of water (the water travels in a current throughout the pot), a hot air balloon (hot air rises, making the balloon rise) , and cup of a steaming, hot liquid (hot air rises, creating steam) are all situations where convection occurs.
Read more on Brainly.com - brainly.com/question/1581851#readmore

7 0

4 years ago

A complete digestive system is found in bears.

GrogVix [38]

Hi! I believe the correct answer is A. Do you have any other questions I can help you with? I would be glad too.

- Amber
<span />

4 0

3 years ago

A 54.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 126 m/s from the top of a cliff

Nikolay [14]

Answer:

a) The initial total mechanical energy of the projectile is 498556.296 joules.

b) The work done on the projectile by air friction is 125960.4 joules.

c) The speed of the projectile immediately before it hits the ground is approximately 82.475 meters per second.

Explanation:

a) The system Earth-projectile is represented by the Principle of Energy Conservation, the initial total mechanical energy ( $E$ ) of the project is equal to the sum of gravitational potential energy ( $U_{g}$ ) and translational kinetic energy ( $K$ ), all measured in joules:

$E = U_{g} + K$ (Eq. 1)

We expand this expression by using the definitions of gravitational potential energy and translational kinetic energy:

$E = m\cdot g\cdot y + \frac{1}{2}\cdot m\cdot v^{2}$ (Eq. 1b)

Where:

$m$ - Mass of the projectile, measured in kilograms.

$g$ - Gravitational acceleration, measured in meters per square second.

$y$ - Initial height of the projectile above ground, measured in meters.

$v$ - Initial speed of the projectile, measured in meters per second.

If we know that $m = 54\,kg$ , $g = 9.807\,\frac{m}{s^{2}}$ , $y = 132\,m$ and $v = 126\,\frac{m}{s}$ , the initial mechanical energy of the earth-projectile system is:

$E = (54\,kg)\cdot \left(9.807\,\frac{m}{s^{2}}\right)\cdot (132\,m)+\frac{1}{2}\cdot (54\,kg)\cdot \left(126\,\frac{m}{s} \right)^{2}$

$E = 498556.296\,J$

The initial total mechanical energy of the projectile is 498556.296 joules.

b) According to this statement, air friction diminishes the total mechanical energy of the projectile by the Work-Energy Theorem. That is:

$W_{loss} = E_{o}-E_{1}$ (Eq. 2)

Where:

$E_{o}$ - Initial total mechanical energy, measured in joules.

$E_{1}$ - FInal total mechanical energy, measured in joules.

$W_{loss}$ - Work losses due to air friction, measured in joules.

We expand this expression by using the definitions of gravitational potential energy and translational kinetic energy:

$W_{loss} = E_{o}-K_{1}-U_{g,1}$

$W_{loss} = E_{o} -\frac{1}{2}\cdot m\cdot v_{1}^{2}-m\cdot g\cdot y_{1}$ (Eq. 2b)

Where:

$m$ - Mass of the projectile, measured in kilograms.

$g$ - Gravitational acceleration, measured in meters per square second.

$y_{1}$ - Maximum height of the projectile above ground, measured in meters.

$v_{1}$ - Current speed of the projectile, measured in meters per second.

If we know that $E_{o} = 498556.296\,J$ , $m = 54\,kg$ , $g = 9.807\,\frac{m}{s^{2}}$ , $y_{1} = 297\,m$ and $v_{1} = 89.3\,\frac{m}{s}$ , the work losses due to air friction are:

$W_{loss} = 498556.296\,J -\frac{1}{2}\cdot (54\,kg)\cdot \left(89.3\,\frac{m}{s} \right)^{2} -(54\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (297\,m)$

$W_{loss} = 125960.4\,J$

The work done on the projectile by air friction is 125960.4 joules.

c) From the Principle of Energy Conservation and Work-Energy Theorem, we construct the following model to calculate speed of the projectile before it hits the ground:

$E_{1} = U_{g,2}+K_{2}+1.5\cdot W_{loss}$ (Eq. 3)

$K_{2} = E_{1}-U_{g,2}-1.5\cdot W_{loss}$

Where:

$E_{1}$ - Total mechanical energy of the projectile at maximum height, measured in joules.

$U_{g,2}$ - Potential gravitational energy of the projectile, measured in joules.

$K_{2}$ - Kinetic energy of the projectile, measured in joules.

$W_{loss}$ - Work losses due to air friction during the upward movement, measured in joules.

We expand this expression by using the definitions of gravitational potential energy and translational kinetic energy:

$\frac{1}{2}\cdot m \cdot v_{2}^{2} = E_{1}-m\cdot g\cdot y_{2}-1.5\cdot W_{loss}$ (Eq. 3b)

$m\cdot v_{2}^{2} = 2\cdot E_{1}-2\cdot m \cdot g \cdot y_{2}-3\cdot W_{loss}$

$v_{2}^{2} = 2\cdot \frac{E_{1}}{m}-2\cdot g\cdot y_{2}-3\cdot \frac{W_{loss}}{m}$

$v_{2} = \sqrt{2\cdot \frac{E_{1}}{m}-2\cdot g\cdot y_{2}-3\cdot \frac{W_{loss}}{m} }$

If we know that $E_{1} = 372595.896\,J$ , $m = 54\,kg$ , $g = 9.807\,\frac{m}{s^{2}}$ , $y_{2} =0\,m$ and $W_{loss} = 125960.4\,J$ , the final speed of the projectile is:

$v_{2} =\sqrt{2\cdot \left(\frac{372595.896\,J}{54\,kg}\right)-2\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (0\,m)-3\cdot \left(\frac{125960.4\,J}{54\,kg}\right) }$

$v_{2} \approx 82.475\,\frac{m}{s}$

The speed of the projectile immediately before it hits the ground is approximately 82.475 meters per second.

7 0

3 years ago