You are asked to calculate the volume of a cylindrical rod of copper.You have used calipers to measure the dimensions of the rod, and haveassigned an error to each measurement. You measured the length of therod to be 0.4 ± 0.2 cm and the radius of the rod to be 8.5 ± 1.4 cm.What is the error in your calculated volume?

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You are attending a county fair with your friend from you physics class. While walking around the fairgrounds, you discover a new game of skill. A thin rod of mass M=0.500 kg and length l=2.00 m hangs from a friction-free pivot at its upper end as shown in Figure.The front surface of the rod is covered with velcro. You are to throw a Velcro-covered ball of mass m=1.0kg at the rod in an attempt to make it swing backward and rotate all the way across the top. The ball must stick to the rod at all times after striking it. If you cause the rod to rotate over the top position, you win a stuffed animal. Your friend volunteers to try his luck. He feels that the most torque would be applied to the rod by striking it at its lowest end. While he prepares to aim at the lowest point on the rod, you calculate how fast he must throw the ball to win the stuffed animal with this technique.

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A very thin glass rod 4 meters long is rubbed all over with a silkcloth. It gains a uniformly distributed charge 1.6X10^â6 C. Twosmall spherical rubber balloons of radius 1.2 cm are rubbed allover with wool. They each gain a uniformly distributed charge of-8X10^â8 C. The balloons are near the midpoint of the glass rod,with their centers 3 cm from the rod. The balloons are 2 cm apart(4.4 cm between centers).

(a) Find the net electric field at the location marked by the X,0.6 cm to the right of the center of the left balloon. Things tothink about: Which objects make nonzero contributions to E field atthis location? What are the correct distances from sources to theobservation location? What is the direction of E field due to therod? (The drawing is not to scale; read the problem statementcarefully. Assume the +x axis is to the right, the +y axis is up,and the +z axis is out.)

E = ________ N/C

(b) What approximations did you make, if any? Which apply(1-4)?
1. Neglect polarization of balloons.
2. Use approximate formula for electric field of a chargedspherical shell.
3. Neglect polarization of rod.
4. Assume distance to observation location is small compared tolength of rod.

(c) Next a proton is placed at that same location (marked by thex). What is the force acting on the proton?

F = ________ N

Note: in parts (a) and (c) there should be an arrow over the"E" and the "F" but the custom equation function would not workproperly.

A quantity is measured 100 times, and, after calculating themean, thestandard deviation, and the standard error on the mean,and assuming the errors on the individual measurements are allrandom, you come to the conclusion that your best value, andstandard error on the mean, are X = 21.0 +/- 0.4

This is fine, but youâd really like to have a final accuracy of0.1 cm. So you take more measurements. Assuming that in the secondbunch of measurements, any given measurement has about as muchrandom error as any given measurement in your original 100measurements, how many measurements should you make, in total, sothat the standard error on the average of all your measurements is0.1 cm

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