Groovin' and Spinnin'

Some practice for the circular motion and gravity test . . .

1. A salad spinner is a cylinder with holes in it that is spun to dry lettuce placed in the spinner.  Mrs. M's spinner has a diameter of 21.0 cm and is spun at a frequency of 9.00 Hz.  Suppose a 1.5 gram leaf of lettuce is stuck against the side of the spinner.  (a) Find the period of the motion.  (b) Find the velocity of the leaf.  (c) Find the acceleration of the leaf.  (d) Find the net force on the leaf.  (e) Find the distance the leaf travels during 45 seconds of spinning. 

2. Explain why the device described above is effective at drying salad.  In other words why is the water "slung" off of the lettuce?  Incorporate physics laws, concepts, etc. in your answer.

3. A wooden block with mass 17.0 grams is placed on a wooden disc rotating at 45.0 rpm.  The coefficient of static friction is 0.40.  What is the maximum distance from the center of the rotating disc that the block can be placed where it will not slip and slide off?

Questions 4 and 5 refer to data from a popular car magazine:

	Mazda Miata	Dodge Viper
Mass	1080 kg	1547 kg
Zero to 60 mph (26.8 m/s)	7.9 s	4.0 s
Top Speed	55.0 m/s (123 mph)	79.1 m/s (177 mph)
Handling (91 m dia. skidpad)	0.89 g	0.97 g
Smallest turn radius	3.73 m	5.21 m
Braking 70 mph (31.3 m/s) to 0	53.0 m	47.9 m

4. (a) Which car, the Miata or the Viper, had the highest speed on the skid pad?  Calculate this speed.  (b) Use other data from the table to determine the maximum amount of friction acting against that car during its skid pad test.

5. Challenge problem:  Using the same information determine which of these two cars could make a U-turn in the shortest amount of time.  Calculate this amount of time.  Assume the U-turn is essentially a semicircular path followed on level pavement.  Also assume that the car has unlimited space in which to make the turn. (i.e. The radius of the turn could be anything - but what will result in the quickest U-turn?). 

6. The Magellan space probe was placed into orbit around the planet Venus in 1992.  Its mission was to map the surface of Venus using radar.  For optimum results the probe was to orbit at an altitude of 4370 km.  The mass of Venus is 4.87 x 10²⁴ kg and its radius is 6100 km.  (a) In order to place it into this orbit what speed was required?  (b) What was the orbital period in hours?

7. Challenge problem:  According to Newton's 3rd Law if the earth pulls on the moon then the moon will pull on the earth with equal force in the opposite direction.  This is true!  Accordingly the earth must accelerate.  The result is that the center of the earth moves in a circular path and the earth "wobbles" with a period equal to that of the moon's motion:  27.3 days.  Find the radius of this circle in which the earth moves.  The distance to the moon is 384 Mm.  Mass of the moon is 7.35 x 10²² kg.  Mass of earth is 5.97 x 10²⁴ kg.

8. A 1.50 kg cart is free to roll without friction on a horizontal track and is attached to a horizontal spring with constant k = 2.50 N/m such that the force of the spring is zero at x = 0.0.  The cart is positioned at x = 30.0 cm, 0.0° and released from rest.  (a) Determine the cart’s initial acceleration just as it is released.  (b) Determine the period of the cart’s oscillation.  (c) Determine the cart’s average speed for one complete cycle.  (d) How much mass would need to be added to the cart in order to double its period?

Answers for the numerical problems:  (Note these are not in the order of the questions – think of this as a “matching” activity!)

4.50 kg

0.18 m

267 m

4.69 Mm

0.247 m/s

5.94 m/s tangent to the circle

5570 m/s

21 m/s

0.500 m/s², 180.0°

336 m/s² toward the center

0.504 N toward the center

14.7 kN

0.111 s

2.05 s

4.87 s

3.28 h