Quiz #1

Name:

This quiz is due at the beginning of class on the 15th of October (Wednesday). You are on your honor not to consult others or reference materials in the completion of this quiz. This includes textbooks and notes. Please note that there are two sides to the quiz.

1.) A pail of water is whirled in a vertical circle of radius r. Draw a free body diagram of the pail at the top of the circle. If its speed is at the top of the circle, find the force exerted on the water by the pail at the top of the circle. Also find the minimun value of for which the water will remain in the pail. If we assume that the length from your shoulder to the water in the pail is approximately 1 m, then what is the maximum period of revolution that the pail can have to keep the water in the pail?

Solution:

The only forces acting on the water are the weight of the water and the normal force exerted by the pail on the water. The water has an acceleration inward towards the center of the circle of an amount . Summing the forces yields

so, solving for the Normal force we find that

Now, to find the minimum velocity that we can whirl the pail around, we can set the normal force of the pail on the water to be equal to zero. This is the condition where the pail just reaches free fall. Solving for yields

Furthermore, since the period of revolution is given by the circumference of the circle divided by the velocity of the object going around the circle, we can find the maximum period of the bucket by substituting in .

and substituting in the value for r, we find that

.

2.) Two blocks are stcked on top of one another on a level table. The mass of the lower block is greater than the mass of the upper block. Draw a separate free-body diagram of each block in the space below. Be sure to describe each force, tell the name of the object each force is acting on, and what object is exerting each force. Which forces in the diagrams have equal magnitudes, if any?

Solution:

**fig**

The normal force on the upper block by the lower block and the force of the upper block on the lower block are Newton's force pairs and therefore have equal magnitudes. Also the magnitude of the force of gravity acting on the upper block has the same magnitude as these others. The Normal force on the lower block is acting from the table on the lower block and the force of gravity acts on each block by the earth.