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3 years ago

How do you find potienal energy

1 answer:

3 0

For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity and h is the height in meters.Watch that gravitational potential energy has the same units as kinetic energy.

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(III) A baseball is seen to pass upward by a window with a vertical speed of If the ball was thrown by a person 18 m below on th

Ghella [55]

Answer:

Assuming that the vertical speed of the ball is 14 m/s we found the given values:

a) V₀ = 23.4 m/s

b) h = 27.9 m

c) t = 0.96 s

d) t = 4.8 s

Explanation:

a) Assuming that the vertical speed is 14 m/s (founded in the book) the initial speed of the ball can be calculated as follows:

$V_{f}^{2} = V_{0}^{2} - 2gh$

Where:

$V_{f}$ : is the final speed = 14 m/s

$V_{0}$ : is the initial speed =?

g: is the gravity = 9.81 m/s²

h: is the height = 18 m

$V_{0} = \sqrt{V_{f}^{2} + 2gh} = \sqrt{(14 m/s)^{2} + 2*9.81 m/s^{2}*18 m} = 23.4 m/s$

b) The maximum height is:

$V_{f}^{2} = V_{0}^{2} - 2gh$

$h = \frac{V_{0}^{2}}{2g} = \frac{(23. 4 m/s)^{2}}{2*9.81 m/s^{2}} = 27.9 m$

c) The time can be found using the following equation:

$V_{f} = V_{0} - gt$

$t = \frac{V_{0} - V_{f}}{g} = \frac{23.4 m/s - 14 m/s}{9.81 m/s^{2}} = 0.96 s$

d) The flight time is given by:

$t_{v} = \frac{2V_{0}}{g} = \frac{2*23.4 m/s}{9.81 m/s^{2}} = 4.8 s$

I hope it helps you!

3 0

4 years ago

An object's buoyant force and weight mean the same thing. A. True B. False

german

Answer:

False

Explanation:

No. The buoyant force on an object is the portion of its weight that appears to vanish

when the object is in any fluid (could be either a liquid or a gas).

If the object happens to float in a particular fluid, then the buoyant force at that moment

is equal to the object's weight.

Notice that the buoyant force on an object will be different in different fluids.

6 0

3 years ago

A tennis ball is dropped from a height of 10.0 m. It rebounds off the floor and comes up to a height of only 4.00 m on its first

Dominik [7]

Answer:

a) $V=14.01 m/s$

b) $V=8.86 \, m/s$

c) $t = 2.33s$

Explanation:

Our most valuable tool in solving this problem will be the conservation of mechanical energy:

$E_m = E_k +E_p$

That is, mechanical energy is equal to the sum of potential and kinetic energy, and the value of this $E_m$ mechanical energy will remain constant. (as long as there is no dissipation)

For a point particle, we have that kinetic energy is:

$E_k = \frac{1}{2} m \, V^2$

Where m is the mass, and V is the particle's velocity,

Potential energy on the other hand is:

$E_p= m\, g\, h$

where g is the acceleration due to gravity ( $g=9.81 \, m/s^2$ ) and h is the height of the particle. How do we define the height? It's a bit of an arbitrary definition, but we just need to define a point for which $h=0$ , a "floor". conveniently we pick the actual floor as our reference height, but it could be any point whatsoever.

Let's calculate the mechanical energy just before the ball is dropped:

As we drop the ball, speed must be initially zero, and the height from which we drop it is 10 meters, therefore:

$E_m = \frac{1}{2}m\,0^2+ mg\cdot 10 \,m\\E_m=mg\cdot10 \, m$

That's it, the actual value of m is not important now, as we will see.

Now, what's the potential energy at the bottom? Let's see:

At the bottom, just before we hit the floor, the ball is no longer static, it has a velocity V that we want to calculate, on the other hand, it's height is zero! therefore we set $h=0$

$E_m = \frac{1}{2}m\,V^2+ mg\cdot 0\\\\E_m = \frac{1}{2}m\,V^2$

So, at the bottom, all the energy is kinetic, while at the top all the energy is potential, but these energies are the same! Because of conservation of mechanical energy. Thus we can set one equal to the other:

$E_m = \frac{1}{2}m\,V^2 = mg\cdot 10m\\\\\\ \frac{1}{2}m\,V^2 = mg\cdot 10m\\\\V = \sqrt[]{2g\cdot 10m} \\$

And so we have found the velocity of the ball as it hits the floor.

$V = \sqrt[]{2g\cdot 10m}=14.01\, m/s$

Now, after the ball has bounced, we can again do an energy analysis, and we will get the same result, namely:

$V = \sqrt[]{2g\cdot h}$

where h is the maximum height of the ball, and v is the maximum speed of the ball (which is always attained at the bottom). If we know that now the height the ball achieves is 4 meters, plugging that in:

$V = \sqrt[]{2g\cdot 4m} =8.86 \, m/s$

Now for C, we need to know for how long the ball will be in the air from the time we drop it from 10 meters, and how long it will take the ball to reach its new maximum height of 4 meters.

As the acceleration of gravity is a constant, that means that the velocity of the ball will change at a constant rate. When something changes at a constant rate, what is its average? It's the average between initial and final velocity, look at diagram to understand. The area under the Velocity vs time curve is the displacement of the ball, and:

$V_{avg}\cdot t=h\\t=h/V_{avg}$