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gavmur [86]
3 years ago
11

You throw a baseball (mass 0.145 kg) vertically upward. It leaves your hand moving at 12.0 m/s. Air resistance can be neglected.

At what height above your hand does the ball have half as much upward velocity? Express your answer with the appropriate units.
Physics
1 answer:
Andru [333]3 years ago
4 0

Answer:

The ball will have an upward velocity of 6 m/s at a height of 5.51 m.

Explanation:

Hi there!

The equations of height and velocity of the ball are the following:

y = y0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

y = height at time t.

y0 = initial height.

v0 = initial velocity.

t = time.

g = acceleration due to gravity (-9.81 m/s² considering the upward direction as positive).

v = velocity of the ball at time t.

Placing the origin at the throwing point, y0 = 0.

Let´s use the equation of velocity to obtain the time at which the velocity is 12.0 m/s / 2 = 6.00 m/s.

v = v0 + g · t

6.00 m/s = 12.0 m/s -9.81 m/s² · t

(6.00 - 12.0)m/s / -9.81 m/s² = t

t = 0.612 s

Now, let´s calculate the height of the baseball at that time:

y = y0 + v0 · t + 1/2 · g · t²     (y0 = 0)

y = 12.0 m/s · 0.612 s - 1/2 · 9.81 m/s² · (0.612 s)²

y = 5.51 m

The ball will have an upward velocity of 6 m/s at a height of 5.51 m.

Have a nice day!

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On a tiny scale, what happens to an initially neutral object’s mass when it gains a net positive charge through the exchange of electrons? (<em>the mass will decrease by a very small factor</em>)

(b) What happens to the mass of an initially neutral object when it gains a net negative charge through the exchange of electrons?  (<em>The mass will increase by a very small factor</em>)

Explanation:

(a) On a tiny scale, what happens to an initially neutral object’s mass when it gains a net positive charge through the exchange of electrons? (<em>the mass will decrease by a very small factor</em>)

The mass of an atom is given by the sum of the masses of the protons, neutrons and electrons. Electrons has lower mass than protons and neutrons, so they have a minor contribution to the total mass of the atom.    

When an object is electrically neutral it means that it has the same number of protons and electrons. For the case of an object positively charged, the rate of protons is greater than the number of electrons. That means that atom lose electrons so the mass will decrease in a very small factor.

(b) What happens to the mass of an initially neutral object when it gains a net negative charge through the exchange of electrons?  (<em>The mass will increase by a very small factor</em>)

For the case when the object is negatively charged, it means that the atom gains electrons from another object, leading to the conclusion that the mass of the atom will increase in a very small factor.  

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Similarly, let F_1 and F_2 denote the size of the force on the two pistons. Since the person is placing all her weight on the first piston:

F_1 = W = m \cdot g = 50\; \rm kg \times 9.81 \; \rm kg \cdot N^{-1} =495\; \rm N.  

Since both pistons fit into cylinders, the two contact surfaces must be circles. Keep in mind that the area of a square is equal to \pi times its radius, squared:

  • \displaystyle A_1 = \pi \times \left(\frac{1}{2} \times 3.0\right)^2 = 2.25\, \pi\;\rm cm^{2}.
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By Pascal's Law, the pressure on the two pistons should be the same. Pressure is the size of normal force per unit area:

\displaystyle P = \frac{F}{A}.

For the pressures on the two pistons to match:

\displaystyle \frac{F_1}{A_1} = \frac{F_2}{A_2}.

F_1, A_1, and A_2 have all been found. The question is asking for F_2. Rearrange this equation to obtain:

\displaystyle F_2 = \frac{F_1}{A_1} \cdot A_2 = F_1 \cdot \frac{A_2}{A_1}.

Evaluate this expression to obtain the value of F_2, which represents the force on the piston with the larger diameter:

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°K = (°F - 32) × 5/9 + 273

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Same procedure to Levine

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Then, the coefficient of performance is the energy Q_L drawn from the cold reservoir as heat divided by work done,

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I hope it helps you!

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