Question

Calculate the force necessary to keep a mass 0.2kg moving in a horizontal circle of radius 0.5m with a period of 0.5s. What is the direction of the force?

Answer 1

Question #73910, Physics / Mechanics | Relativity|

Calculate the force necessary to keep a mass $0.2\mathrm{kg}$ moving in a horizontal circle of radius $0.5\mathrm{m}$ with a period of 0.5s. What is the direction of the force?

Need to find: $\mathbf{F}_{\mathrm{c}} - ?$

$$\mathrm {m} = 2 \mathrm {k g}$$ $$\mathrm {R} = 0. 5 \mathrm {m}$$ $$\mathrm {T} = 0. 5 \mathrm {s}$$

Solution:

From Newton's second law a force will cause an $-\overrightarrow{F_c} = m \cdot \vec{a}$ .

The acceleration of an object moving in a circle can be determined by either two of the following equations.

$$a = \frac {v ^ {2}}{R}$$

The speed of an object moving in a circle is given by the following equation -

$$v = \frac {2 \cdot \pi \cdot R}{T}, a = \frac {4 \cdot \pi^ {2} \cdot R}{T ^ {2}}$$

Hence, $F_{c} = m \cdot \frac{4 \cdot \pi^{2} \cdot R}{T^{2}}$ , $F = kg \cdot \frac{m}{s^{2}} = N$ , $F = 2 \cdot \frac{4 \cdot \pi^{2} \cdot 0.5}{0.5^{2}} \approx 160$

Answer: $\mathrm{F_c} = 160\mathrm{N}$ . The force is directed towards the center.