Question

Your salad spinner has a diameter of 26.9 cm and a height of 17.5 cm. The mass is 380 g. The coefficient of friction between the counter and the spinner is .69. A similar spinner spins at max 600 rpm. Suppose you place some lettuce into one side of the basket, pump the salad spinner until the basket is spinning at top speed and then remove your hand. What is the max amount of lettuce that can be in the basket such that the spinner does not slip when you remove your hand? Answer in grams

Answer 1

Answer:

The maximum amount of lettuce that will not make the spinner slip = 4.84 g

Explanation:

Diameter, D = 26..9 cm

Radius, r = D/2 = 26.9/2 = 13.45 cm = 0.1345 m

Height, h = 17.5 cm = 17.5/100 = 0.175 m

Mass, m = 380 g

Coefficient of friction, $\mu = 0.69$

Angular speed, $w = 600 rpm = 600 * (2\pi /60)$

$w = 62.83 rad/s$

The spinner will not slip only when the centripetal force does not exceed the force between the spinner and the basket

F = μmg.........(1)

$F_{c} = m_{l} w^{2} r$........(1)

Equating (1) and (2)

$\mu mg = m_{l} w^{2} r\\0.69 * 380 * 9.81 = m_{l} * 62.83^{2} * 0.1345$

$2572.182 = 530.95 m_{l} \\ m_{l} = \frac{2572.182}{530.95} \\ m_{l} = 4.84 g$