# Question 471de

Apr 3, 2017

$v = 5 \sqrt{5} \text{ } \frac{m}{s}$

#### Explanation:

${F}_{c} : \text{centripetal force(the blue vector)}$

$v : \text{velocity (the red vector)}$

$m : \text{mass of object }$

$r : \text{radius}$

$\text{given :}$

${F}_{c} = 250 N$

$m = 4 k g$

$r = 2 m$

v=?#

$\text{The centripetal force can be calculated using the fallowing formula.}$

$\text{please notice that; }$

• The centripetal force has directed toward the orbit center.
• The velocity vector is perpendicular to the centripetal corce vector.
• The velocity vector is tangent to the orbit.

${F}_{c} = m \cdot {v}^{2} / r$

$250 = \cancel{4} \cdot {v}^{2} / \cancel{2}$

$250 = 2 {v}^{2}$

${v}^{2} = \frac{250}{2}$

${v}^{2} = 125$

${v}^{2} = 25 \cdot 5$

$\sqrt{{v}^{2}} = \sqrt{25 \cdot 5}$

$v = 5 \sqrt{5} \text{ } \frac{m}{s}$