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RoseWind [281]
2 years ago
10

A rotating turntable (rt=4.50 m) is rotating at a constant rate. At the edge of the turntable is a mass (m = 3.00 kg) on the end

of a 5.00 m - long string (L). If theta = 40.0o,determine:
Physics
1 answer:
navik [9.2K]2 years ago
4 0

The magnitude of the tension in the string is 9.31 N.

<h3>Tension in the string</h3>

The magnitude of the tension in the string in the horizontal circle formed by the turn table is calculated as follows;

T = Fcos(θ)

where;

  • F is centripetal force
  • θ is inclination of the string

T = \frac{mv^2}{r} \times cos(\theta)\\\\T = \frac{3 \times 4.5^2}{5} \times cos(40)\\\\T = 9.31 \ N

Thus, the magnitude of the tension in the string is 9.31 N.

The complete question is below:

A rotating turntable (rt=4.50 m) is rotating at a constant rate. At the edge of the turntable is a mass (m = 3.00 kg) on the end of a 5.00 m - long string (L). If theta = 40.0o,determine the magnitude of the tension in the string.

Learn more about tension in horizontal circle here: brainly.com/question/12803719

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A charge of 3.20 μC is held fixed at the origin. A second charge of 3.20 μC is released from rest at the position (1.25 m, 0.570
siniylev [52]

Answer:

a) v = 7.137 m/s and b) r = 1.832\ m

Explanation:

We have to analyze this problem from the point of view of energy conservation. In this case there are two kind of energy, electric potential energy and kinetic energy. First, at t = t_1 there isn't relative movement between the two charges, so kinetic energy is zero and the total energy (E_T = E_p + E_k) is just potential.

E_T = E_p = \frac{k q_1 q_2}{r}

where k is the Coulomb constant, q_1 and q_2 are the two interacting charges, and r is the distance between them.

Considering the fixed charge at (x1,y1) = (0,0) and the second one at (x2, y2) = (1.25, 0.57), the initial distance is

r = \sqrt{(x_2-x_1)^2 + (y_2- y_1)^2} = \sqrt{(1.25)^2 + (0.57)^2} = 1.374\ m, then if

k =8.987\times 10^9 N m^2/C^2 and   q_1 = q_2 =3.2\times 10^{-6} C,

E_T = E_p = \frac{k q_1 q_2}{r} = \frac{8.987\times 10^9 * 3.2\times 10^{-6}*3.2\times 10^{-6}}{1.374} = 6.698 \times 10^{-2} Nm.  

Now, at t = t_2, r \rightarrow \infty  and E_p \rightarrow 0. This means all the energy is kinetic

E_T = E_k = \frac{1}{2}mv_f^2, so

v_f = \sqrt{2E_T/m} =\sqrt{2 *6.698 \times 10^{-2} /0.00263} = 7.137 m/s (mass in Kg).

That would be the velocity when the second charge moves infinitely far from the origin.

For the second part we have that v = v_f/2, so kinetic energy is

E_k = \frac{1}{2}mv^2 = 1.674 \times 10^{-2} Nm

and potential energy is

E_p = E_T - E_k = 6.698 \times 10^{-2} - 1.674 \times 10^{-2} = 5.024 \times 10^{-2} Nm

so the distance is

r = \frac{k q_1 q_2}{E_p} = 1.832\ m

   

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