Object A has a mass of 10 kg and is moving at a velocity of 2.0

A force of 10 N causes a spring to extend by 20 mm. Find a) the spring constant of the spring in N/m b) the extension of the spr

suter [353]

(a) The spring constant is 500 N/m.

(b) The extension of the spring when 25 N force is applied is 0.05 m.

(c) The applied force to cause an extension of 5 mm is 2.5 N.

The given parameters:

Applied force, F = 10 N
Extension of the spring, x = 20 mm

The spring constant is calculated as follows;

$F = kx\\\\k = \frac{F}{x} \\\\k = \frac{10}{20 \times 10^{-3}} \\\\k = 500 \ N/m$

The extension of the spring when 25 N force is applied is calculated as follows;

$F = kx\\\\x = \frac{F}{k} \\\\x = \frac{25}{500} \\\\x = 0.05 \ m$

The applied force to cause an extension of 5 mm is calculated as follows;

$F = kx\\\\F = 500 \times 5 \times 10^{-3}\\\\F = 2.5 \ N$

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A capacitor with initial charge q0 is discharged through a resistor. a) In terms of the time constant τ, how long is required fo

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It would take $\tau(\ln 9 - \ln 8)$ time for the capacitor to discharge from $q_0$ to $\displaystyle \frac{8}{9} \, q_0$ .

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In an RC circuit, a capacitor is connected directly to a resistor. Let the time constant of this circuit is $\tau$ , and the initial charge of the capacitor be $q_0$ . Then at time $t$ , the charge stored in the capacitor would be: