Exploration - Teacher Information

Helpful Hints:

1. This exploration allows the students to review the definition of acceleration. Emphasize that acceleration and velocity are vector quantities that may not change in magnitude, direction or both.

2. Record players/turntables can be found in your school's media center. Some may be located at garage sales. They have 3-4 speeds depending on the individual record player.

3. A 29 cm (11.5-inch) diameter circle should be cut out of foam board or ¼ inch veneer. Cut a 3/8-inch hole in the center of the circle to fit on the spindle of the turntable.

4. It is important in this lab that the LabPro and Accelerometer are firmly secured to the turntable. Be sure to secure the extra wire of the accelerometer by either wrapping it around the LabPro or tying it with a rubber band.

5. It is important that the arrow on the accelerometer is pointing inward toward the center of the turntable or your acceleration values will be low.

6. The mass used in the exploration should be a slotted mass. If you do not have slotted masses, use masses that are low and wide to prevent it from falling over while the turntable is in motion.

7. It is not necessary to calibrate the accelerometer. It is important that you zero the sensor on the turntable if you calibrated it.

Answers to Explorations

Discussion I

1. Ask students to recount their observations.

2. Is the linear speed of the mass constant or changing? [Linear speed is constant.]

3. Is the velocity of the mass constant or changing? [At a constant linear speed around a curve the direction is always changing.] Is the acceleration of the mass constant, zero, or unchanging? [The acceleration is constant.]

4. If there is acceleration, what is its direction? [Use guided questioning to make sure the students understand that the direction of acceleration is always toward the center of the circle.]

5. What keeps the mass on the turntable? [Friction keeps the mass on the turntable.]

Discussion II

1. Ask the students to recount their observations. [Each mass is linear moving at a different constant speed.]

2. Did both masses travel at the same linear speed? [The 20g mass at 12 cm has a greater linear speed than the 20g mass at 5 cm.] Justify your answer. [The greater the distance from the center, the greater the radius. Therefore, the greater circumference in the same amount of time will have a greater speed.]

Discussion III

1. Ask the students to recount their observations. [The 20g mass travels at a different linear speed at each rpm. At 78 rpm, the mass flew off at a tangent.]

2. Did the mass remain on the turntable at all speeds? [No, the 20g mass flew off at 78 rpm.] How can you explain what you saw? [The frictional force was not great enough to keep the mass on a circular path. Inertia caused the mass to move in a straight line.]

3. Did the mass undergo more, less, or the same acceleration at the different speeds? The mass undergoes more acceleration at the larger speeds.] Justify your answer. [The 20g mass flying off at the greater speed justifies this.]

4. What variables do you think might affect the acceleration? [Probably will come up with mass, speed, radius, friction.]

Discussion IV

1. If you are moving in a straight line, does speeding up while moving in the positive direction correspond to a positive or a negative acceleration? [An increase in position over time gives a positive change in velocity. A positive change in velocity over time is a positive acceleration.] If you are slowing down while moving in the positive direction does this correspond to a positive or a negative acceleration? [A decrease in position over time gives a negative change in velocity. A negative change in velocity over time is a negative acceleration.] You should base your answers on the definition of position, velocity, and acceleration.

2. In your graph of acceleration vs. time, the Accelerometer has to first speed up in the direction of the arrow before slowing down later. Is the acceleration in the direction of the arrow read as positive or negative? [Speeding up in + direction + Slowing down in + direction - Acceleration in direction of arrow reads +.]

EXPLORATIONS V - VII SHOULD BE DONE IN COOPERATIVE GROUPS. IN EXPLORATION VI MAKE SURE EACH OF FOUR GROUPS ARE ASSIGNED DIFFERENT ANGULAR SPEEDS. IT IS ONLY NECESSARY FOR EACH GROUP TO DO ONE OF THE ANGULAR SPEEDS. THE GROUPS SHOULD THEN SHARE THEIR DATA WITH THE REST OF THE GROUPS.

Discussion Vf f f f f f f f f ff f f f f f f

1. What kind of relationship exists between the centripetal acceleration and the square of the angular speed? [There is a linear relationship between the centripetal acceleration and the square of the angular speed.]

2. What are the units of the slope? [The units of the slope is in meters.]

3. What quantity does the slope represent? [The slope represents a length. The centripetal acceleration is equal to the radius times the square of the angular velocity]

4. Does the value of the slope correspond to any measurement in this exploration? [The slope corresponds to the radius.]

Data Table:

The following graph was done on a turntable with only two speeds. Many turntables can be found with up to 4 different speeds. At least three speeds should be done to obtain better data analysis.

Discussion VI

1. What kind of relationship did you find between centripetal acceleration and the radius? [There is a linear relationship between the centripetal acceleration and the radius.]

2. Does the slope correspond to any quantity in this experiment? [Since the units of the slope is s^-2, the slope value corresponds to the square of the angular speed.] How about the square root of the slope? [The square root of the slope corresponds to the angular speed.]

Data Table:

Discussion VII

1. What kind of relationship did you find between centripetal acceleration and the mass? [There is no relationship between the centripetal acceleration and mass because the graph is not a horizontal line.] Justify your answer. [Mass does not affect the centripetal acceleration.]

Data Table:

Discussion V - VII The mathematical relationship found by the students should be a_c = wr².