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3 years ago

Total amount of kinetic and potential energy in a system

1 answer:

6 0

The Total Mechanical Energy
As already mentioned, the mechanical energy of an object can be the result of its motion (i.e., kinetic energy) and/or the result of its stored energy of position (i.e., potential energy). The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy.

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A 4.0kg bowling ball sliding to the right at 8.0 m/s has an elastic head-on collision with another 4.0 kg bowling ball initially

Kisachek [45]

We use the formula :

m1v1i + m2v2i = m1v1f + m2v2f

Substituting the values in:

4.0kg*8.0m/s + 4.0kg*0m/s = 4.0kg*0m/s +4.0kg*v2f

Calculating this we get:

32.0kg*m/s + 0kg*m/s = 0kg*m/s + 4.0kg*v2f

Rearrange for v2f:

v2f = $\frac{32.0kg*m/s}{4.0kg}$

This gives us 8.0 m/s as the final velocity of the second ball.

Since the collision is assumed to be elastic it means that the kinetic energy must be equal before and after the collision.

This means we use the formula:

Ek = $\frac{1}{2} *m*v^{2}$ + $\frac{1}{2} *m*v^{2}$ = $\frac{1}{2} *m*v^{2}$ + $\frac{1}{2}*m*v^{2}$

Substituting in values:

Ek = 0.5*4.0kg*(8.0m/s)^2 + 0.5*4.0kg*(0m/s)^2 = 0.5*4.0kg*(0m/s)^2 + 0.5*4.0kg*(8.0m/s)^2

This simplifies to:

Ek= 128J + 0J = 0J + 128J

This shows us that the kinetic energy is equal on each side therefore the collision is Elastic and no energy has been lost.

6 0

2 years ago

A pendulum has 201 J of potential energy at the highest point of its swing. How much kinetic energy will it have at the bottom o

malfutka [58]

<h2>Hello!</h2>

The answer is: 201 J of kinetic energy.

The motion of a pendulum (with no friction considered) is a continuous exchange between potential energy and kinetic energy.

So, at the highest point of its swing, the potential energy will be the maximum potential energy that the pendulum can have and the kinetic energy will be 0 since at max height the speed tends to 0.

On the opposite side, when the pendulum is at the bottom (the lowest point of its swing) the potential energy will be the minimum (tends to 0) but the kinetic energy will be the maximum.

Also, in the pendulum motion, the total energy is conserved, meaning that:

$PE_{h} +KE_{h}=PE_{l} +KE_{l}\\PE=mgh\\KE=\frac{1mv^{2} }{2}$

Where,

PE(h),is the potential energy at the highest point.

KE(h), is the kinetic energy at the highest point.

PE(l), is the potential energy at the lowest point (bottom of pendulum swing).

KE(l), is the kinetic energy at the lowest point (bottom of pendulum swing).

m, is the mass of the object.

g, is the acceleration of gravity.

v, is the speed of the object.

So, what is the energy at the bottom of its swing?

$201J +0=0 +201J\\201J=201J$

So, the pendulum has 201 of kinetic energy at the bottom of its swing.

Meaning that the energy is conserved.

Have a nice day!

7 0

2 years ago

A new company is making security cameras. These security cameras will be different than other security cameras because instead o

babunello [35]

Answer:

Explanation:

4 0

2 years ago

Our Sun shines bright with a luminosity of 3.828x10^26 Watt. Her energy is responsible for many processes and the habitable temp

Sav [38]

Answer:

(a) 1317.44 W/m²

(b) 1.74×10¹⁵ litres of heating oil

(d) Energy storage in the Earth and the air

Explanation:

The parameters given are;

Luminosity of the Sun = 3.828 × 10²⁶ Watt

Distance of the Earth from the Sun, d = 152.06 × 10⁶ km

The radius of the Sun = 696 × 10³ km

The radius of the Earth, $r_E$ = 6730 km

The surface area of the Sun = 12000 × Surface area of the Earth

The surface area of the Sun = 6.09 × 10¹² km²

Cross sectional area of the Earth = 1.27 × 10⁴ m² = 0.0127 km²

By the inverse square law, we have;

$R = \dfrac{Luminosity \, of \, the \, Sun}{4 \pi d^2}$

Where:

R = Solar radiation reaching the Earth

Therefore;

$R = \dfrac{3.828 \times 10^{26}}{4 \times \pi \times (1.5206 \times 10^{11})^2} = 1317.44 \ W/m^2$

Hence, the energy, E, reaching the Earth in a day is given as follows;

E = R × 4×π× $r_E$ ²×60×60×24 = 1317.44 × 4 × π × 6730000² × 60×60×24

E = 6.479×10²² Joules

(b) The number of litres of heating oil is therefore;

6.479×10²² J ÷ (37.3×10⁶ J/litre) = 1.74×10¹⁵ litres of heating oil

0.7 × 6.479×10²² Joules = 4.54×10²² Joules reaches the Earths surface

From Stefan-Boltzmann law, we have;

$T = \left (\dfrac{\left (1 - \alpha \right ) \times R }{4\times \sigma } \right )^{\dfrac{1}{4}}$

Where:

α = 0.3

σ = Stefan-Boltzmann constant = 5.6704×10⁻⁸ W/(m²·K⁴)

Therefore;

$T = \left (\dfrac{\left (1 - 0.3 \right ) \times 1317.44 }{4\times 5.6704 \times 10^{-8} } \right )^{\dfrac{1}{4}} = 252.52 \ K = -20.63 ^{\circ} C$

(d) The heat storage in the Earth and the air

7 0

2 years ago

A skateboard is moving to the right with a velocity of 8 m/s after a steady Gust of wind that last 5 seconds the skateboarder is

Rzqust [24]

The acceleration of the skateboard is $-0.6 m/s^2$ (to the left)

Explanation:

The motion of the skateboard is a uniformly accelerated motion, so we can use the following suvat equation:

$v=u+at$

where

v is the final velocity

u is the initial velocity

a is the acceleration

t is the time

For the skateboard in this problem, choosing right as positive direction, we have:

u = +8 m/s is the initial velocity

v = +5 m/s is the final velocity

t = 5 s is the time

Solving for a, we find the acceleration:

$a=\frac{v-u}{t}=\frac{5-8}{5}=-0.6 m/s^2$

And since the sign is negative, the direction is to the left.

Learn more about acceleration here:

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#LearnwithBrainly

6 0

3 years ago

Total amount of kinetic and potential energy in a system ​

Total amount of kinetic and potential energy in a system