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AnnZ [28]
3 years ago
8

A small cork is charged to +4.50 mC. Find the number of excess elementary charges (protons or electrons)

Physics
1 answer:
Irina-Kira [14]3 years ago
7 0

Answer:

The third choice: 2.81*10^{16} \: \text{protons}

Explanation:

The cork is positively charged, therefore we know tat there must be excess of positively charged protons present.

The charge p^+ of a proton is

p^+ = +1.6*10^{-19}C;

therefore, the number n that makes up a charge of +4.5mC is

n = \dfrac{+4.5mC}{+1.6*10^{-19}C}  = \dfrac{+4.5*10^{-3}C}{+1.6*10^{-19}C}

\boxed{n =2.81*10^{16} \: \text{protons}}

which is the 3rd choice.

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A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves o
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Correct question is;

A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s²)

Answer:

x(t) = 7te^(-2t√2)

Explanation:

We are given;

Weight; W = 8 lbs

mass; m = W/g

g = 32 ft/s²

Thus;

m = 8/32

m = ¼ slugs

From Newton's second law we can write the equation as;

m(d²x/dt²) = -kx - β(dx/dt)

Rearranging this, we have;

(d²x/dt²) + (β/m)(dx/dt) + (k/m)x = 0

Where;

β is damping constant = √2

k is spring constant = W/s

Where s = 8ft - 4ft = 4ft

k = 8/4

k = 2

Thus,we now have;

(d²x/dt²) + (√2/(¼))(dx/dt) + (2/(¼))x = 0

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The auxiliary equation of this is;

m² + (4√2)m + 8 = 0

Using quadratic formula, we have;

m1 = m2 = -2√2

The general solution will be gotten from;

x_t = c1•e^(mt) + c2•t•e^(mt)

Plugging in the relevant values gives;

x_t = c1•e^(mt) + c2•t•e^(mt)

At initial condition of t = 0, x_t = 0 and thus; c1 = 0

Also at initial condition of t = 0, x'(0) = 7 and thus;

Since c1 = 0, then c2 = 7

Thus,equation of motion is;

x(t) = 7te^(-2t√2)

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Answer:

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Now, let's find the force of gravity on Dumbo at the surface of the earth, which would be in magnitude equal to the normal force that the Earth's surface applies on Dumbo.

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