Question

An object of mass 0.30 kg is attached to end of a string and supported by a smooth horizontal surface. The object moves in a horizontal circle of radius 0.50 m a uniform speed of 2.0 m/s. Calculate,

(i) the centripental acceleration,

(ii) the tension in the string.

Answer 1

Answer on Question 68153, Physics, Other

Question:

An object of mass $0.30 \, kg$ is attached to the end of a string and supported by a smooth horizontal surface. The object moves in a horizontal circle of radius $0.50 \, m$ with a uniform speed of $2.0 \, m/s$. Calculate:

(i) the centripetal acceleration

(ii) the tension in the string

Solution:

(i) We can find the centripetal acceleration from the formula:

$$a_c = \frac{v^2}{r},$$

here, $a_c$ is the centripetal acceleration, $v$ is the speed of the object and $r$ is the radius of the circle.

Then, we get:

$$a_c = \frac{v^2}{r} = \frac{\left(2.0 \, \frac{m}{s}\right)^2}{0.50 \, m} = 8 \, \frac{m}{s^2}.$$

(ii) The force of tension in the string provides the necessary centripetal force, so we can write:

$$T = F_c,$$ $$T = m a_c = m \frac{v^2}{r} = 0.30 \, kg \cdot \frac{\left(2.0 \, \frac{m}{s}\right)^2}{0.50 \, m} = 2.4 \, N.$$

Answer:

(i) $a_c = 8 \, \frac{m}{s^2}$.

(ii) $T = 2.4 \, N$.

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