Question

Cheska swung around vertically a 100-gram plumb bob tied in a 50-centimeter nylon string. If the nylon string tension is 20 N at the lowest position, what will be the speed of the plumb bob at this point?​

Answer 1

Answer:

v = 9.75 m/s

Step-by-step explanation:

Use the vertical circular motion formula: T-mg=(mv²)/r

v²=[(T-mg)r]/m

v²=[(20 N - 0.98 kg·m²/s²) 0.5 m]/ 0.1 kg

v²=95.1 m²/s²

*square root both sides of the equation*

v = 9.751922887 m/s or 9.75 m/s

*shoutout to all STEM students in TMCSHS :)

Answer 2

Given:

Mass of plumb bob(m) = 100 g   = 0.1 kg

Length of string(r) = 50 cm  = 0.5 m

Tension in the string at the lowest point (T)= 50 N

Acceleration due to gravity = 10 m/s

To find:

Speed of bob at the lowest point.

Explanation:

The bob is swung vertically in a circle,

Therefore, at the lowest point the bob would experience a force due to gravity that is actually its own weight, that is mg.

To avoid the string from yielding, the tension (T) in the string has to be greater than the force due to gravity(mg) to provide the necessary centripetal force ($\frac{mv^{2} }{r}$).

Hence,  

$T - mg = \frac{mv^{2} }{r}$

Substituting the values, we get

$(20) - 0.1(10) = \frac{(0.1)v^{2} }{0.5}$ ; or

$v^{2}= (19)(5)\\v = 9.74 m/s$  

Final answer :

Hence, the value of velocity at the lowest point shall be 9.74 m/s.