LAB 7. ROTATION 7.1 Problem How are quantities of rotational motion defined? What sort of influence changes an object s rotation? How do the quantities of rotational motion operate? 7.2 Equipment plumb bob, short length of pipe, swivel chair, dumbbells, balance, torque arm, vertical bar with horizontal crossbar, s-hook, hanging weights, gyroscope 7.3 Activities ACTIVITY 1. PLUMB BOB AND PIPE Figure 1. Adjust the length of string between the pipe and the bob. 1. Hold the pipe in one hand and the free end of the string with the other. (See Figure 1.) Swing the bob by the pipe so that the bob travels in a horizontal circle. What direction is the force the pipe applies to the string? In what direction is the force the string applies to the bob? 67
2. Draw a force diagram for the forces acting on the bob as it circles. (The diagram is oriented so that you are looking horizontally at the bob and string, so that both are in the plane of the paper.) Draw the forces as vector arrows originating at the ball and pointing in the directions that the forces act. Draw the lengths of the arrows proportional to the magnitudes of the forces. string bob 3. What is the direction of the net force on the circling bob? (Hint: in what direction does the bob accelerate?) 4. As the bob circles, pull its string into the pipe so that the radius of its path shortens. How is the bob s motion affected? Describe any changes in its speed and path. 5. As the bob circles, feed more string through the pipe so that the radius of its path lengthens. How is the bob s motion affected? 68
ACTIVITY 2. LEVER ARM The lever arm is a non-uniform wooden strut with several attachment points. In this activity, you will suspend it by the eye bolt at B and hang weights from the eye bolt at the narrow end D or from a string loop through the hole A in the wide end to balance it. 1. Use a balance to find the mass M of the lever arm. M = g 2. Find the center of mass of the lever arm by placing it atop a narrow cylinder and repositioning the cylinder until the lever arm balances. Measure and record the distances from the eye bolt at B to positions A, the center of mass C, and the terminal eye bolt at D. x A = cm x B = cm x C = cm 3. Calculate the torque about B from the weight of the lever arm at its center of mass C. Calculate the mass that will produce a torque opposite to this when hung from position A. m A = g 4. Suspend the lever arm by an s-hook through the eye bolt at B. Hang the calculated mass m A from the string loop at A. If the lever arm does not balance perfectly horizontally, check your calculations. 5. Next, you will hang a mass m D from the eye bolt at D. Obtain the mass m D from your instructor. Calculate the mass needed at point A to make the lever arm balance. m D = g m A = g 6. With your instructor as a witness, hang the calculated mass from the string loop at A. If the lever arm does not balance perfectly horizontally, check your calculations. ACTIVITY 3. SWIVEL CHAIR 1. Sit in the swivel chair. Hold the dumbbells in your outstretched arms. Spin yourself, or have a gentle partner spin you. While coasting, pull the dumbbells toward your body. a. How does the force required to move the dumbbells compare to the force required when you are not spinning? 69
b. What happens to your rotational speed? 2. Move the dumbbells back away from your body, so that your arms are again outstretched. What happens to your rotational speed? ACTIVITY 4. GYROSCOPE 1. Place one ball end of the gyroscope frame in the stand. Orient the gyroscope so that its rotational axis is parallel to the ground. Hold the other end of the gyroscope in your hand Spin the rotor clockwise from the perspective looking down the gyroscope axis toward the stand. 2. Release the gyroscope. What does it do? 3. When the gyroscope began to spin, what was the direction of its angular momentum vector? (Evaluate this about the center of mass of the gyroscope.) 4. What is the direction of the torque on the gyroscope from the stand? (Evaluate this about the center of mass of the gyroscope.) 5. What is the direction of the torque on the gyroscope from its weight? (Evaluate this about the center of mass of the gyroscope.) 6. What is the direction of the net torque acting on the gyroscope? (Evaluate this about the center of mass of the gyroscope.) 7. After the net torque acts on the gyroscope for a short time, what is the direction of the change in the gyroscope s angular momentum vector? 8. What should be the new direction of the gyroscope s angular momentum? 9. Was that what you observed? If not, check the directions of all the vectors you evaluated in steps 3 8. 70
LAB 8 PRE-LAB H L W 1. A box with rectangular faces has dimensions L, W, and H. What is the formula for the volume of the box? 2. A lump of stuff has a mass m and volume V. What is the formula for the density of the lump? 3. When an object floats at rest on water, in what direction is the net force acting on it? Upward. Parallel to the surface of the water. Downward. Zero. 4. In which state of matter are the molecules, in general, farthest apart? Solid. Liquid. Gas. 71
LAB 8. THE PROPERTIES OF MATTER 8.1 Problem To understand numerous properties of matter, including elasticity, density, pressure, buoyancy, Archimedes Principle, Pascal's Principle, and gases as substance. 8.2 Background This lab explores several properties of solids, liquids, and gases. Each activity is selfcontained, so you may start the lab at any station and do the activities in any order. Make sure you make all of the needed measurements and finish all the activities during the lab period. The questions and analysis sections can be finished outside of the lab. Note on measuring liquid volumes: Like rulers and meter sticks, graduated cylinders and beakers are subject to parallax errors. To read the volume in a graduated cylinder accurately, you must hold your eyes level with the liquid in the cylinder so that your line of sight is perpendicular to the side of the cylinder. The surface of the liquid will be slightly curved; this is called a meniscus and is caused by surface tension and adhesion forces between the liquid and the sides of the cylinder. Read the level of the bottom of the meniscus. 8.3 Activities SOLIDS The molecules in solids have relatively low mobility; they do not move around but rather vibrate in place. Solids have a fixed volume and generally hold their own shape. Density Density is a measure of how tightly packed a mass is. Density is defined as mass per unit volume. Use the available materials to calculate the density of various objects. EQUIPMENT metal block, triple-beam balance, ruler, meter stick, overflow can (cup with spout), water, graduated cylinder MEASUREMENT 1. Find the mass of the metal block using the triple beam balance (you may need to add the auxiliary weight to the end of the beam). Record this mass here. Measure the block s exterior dimensions as well. Mass Length Width Height 2. Calculate the volume of the block. 73
3. Calculate the density of the block. 4. Fill the overflow can with water to the brim until the water begins to overflow. After the flow stops, place an empty graduated cylinder under the overflow spout. Carefully submerge the metal block in the overflow can, catching all the overflow water in the graduated cylinder. Record the volume of water displaced by the block. (Don t forget the units!) Volume displaced = 5. Use the volume of displaced water to find the volume of the block. (The block and the water it displaces have the same volume unless you splashed or there is an air bubble under the block.) How does this value compare to the volume found in step 2? 6. What would the density of the block be on the moon? 74
LIQUIDS Unlike solids, liquids flow; their molecules are not restricted to fixed positions. Liquids conform to the shape of their vessel, exert force against the vessel, and transmit pressure throughout the liquid. Liquid Pressure EQUIPMENT plastic water jug with three nail valves on the side, basin, water MEASUREMENT 1. Remove the nails from the plastic jug. Draw a diagram of the trajectories of the three streams of water. 2. Draw vectors on your sketch of step 1 showing the directions and relative magnitudes of the forces acting on the side of the jug at each hole. Buoyancy A submarine dives and surfaces by pumping water into or out of its bilge tanks, thereby changing its overall mass and density. To maintain a constant depth, upward buoyant forces due to pressure differences must balance the force due to gravity on the submarine (i.e., its weight). The buoyant force is equal to the weight of the sea water displaced. EQUIPMENT test tube boat, graduated cylinder, metal balls, forceps or needle-nosed pliers, lump of clay, container (beaker) of water, overflow can MEASUREMENT 1. Place the test tube boat in a graduated cylinder that contains some water (the boat s sea). Record the height of the sea in ml. Carefully load the boat by adding 1-gram metal balls one at a time and record in Table 1 the new heights of the sea with each addition. 75
Number of balls Table 1. Balls in a test tube Mass of balls (g) Height of sea (ml) Height change (ml) Water displaced (g) 0 0 0 2. Complete the columns in Table 1. Calculate the mass of additional water displaced with each metal ball loaded. The density of water is 1 g/cm 3, and 1 cm 3 = 1 ml. Compare the mass of water displaced with the mass of the metal balls. Are they the same or not? 3. Fill an overflow can with water to its maximum height. Roll a small lump of clay into a ball and carefully put it into the can. Catch the displaced water in a graduated cylinder. Observe whether the ball sinks or floats. Form the same lump into different shapes to try to make one that floats. Record the volumes of water displaced in Table 2. Mass of lump: g Table 2. Clay lumps Description of clay shape Float or sink? Volume water displaced (ml) Mass water displaced (g) 76