Companion to the reading passage The Pendulum Through History: How a Simple Swing Changed Science. Answer each question, then click Check. Multiple-choice and number questions grade themselves; for written answers, compare yours with the model answer and checklist, then score yourself honestly.
Around 1600, Galileo noticed that a swinging chandelier seemed to take the same time for each swing. A group of students investigated which variables affect the period of a pendulum (the time for one complete back-and-forth swing). They changed one variable at a time and recorded the average period for each trial in Table 1. All release angles were small.
Table 1: Pendulum Trials
| Trial | String Length (m) | Mass of Bob (kg) | Release Angle (°) | Period (s) |
|---|---|---|---|---|
| 1 | 1.00 | 0.10 | 10 | 2.01 |
| 2 | 1.00 | 0.20 | 10 | 2.01 |
| 3 | 1.00 | 0.10 | 5 | 2.01 |
| 4 | 0.50 | 0.10 | 10 | 1.42 |
| 5 | 2.00 | 0.10 | 10 | 2.84 |
Data are representative values for practice.
1. Which row correctly identifies whether each variable affected the period of the pendulum in this investigation?
In 1742, Benjamin Robins measured the speed of musket balls by firing them into a heavy wooden block hanging as a pendulum. Students tested a safe classroom version. A 0.010-kilogram projectile moving horizontally at 199 meters per second strikes a 2.000-kilogram block hanging at rest and becomes embedded in it. Table 2 shows the results.
Table 2: Ballistic Pendulum Trial
| Quantity | Value |
|---|---|
| Mass of projectile | 0.010 kg |
| Speed of projectile just before the collision | 199 m/s |
| Mass of block | 2.000 kg |
| Speed of block and projectile just after the collision | 0.990 m/s |
| Maximum vertical rise of block and projectile | 0.050 m |
Data are representative values for practice.
2. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
After the collision, the block and projectile swing upward together until they momentarily stop at their maximum height. Consider the Earth–block–projectile system. Position A is the lowest point, just after the collision. Position B is halfway up to the maximum height (0.025 m above Position A). Position C is the maximum height. The lowest point is the zero level for gravitational potential energy, and friction and air resistance are negligible during the swing.
3. Substitute numerical values into a mathematical representation that can be used to determine the gravitational potential energy of the Earth–block–projectile system at Position C. Then calculate it.
4. The energy bar graph for the Earth–block–projectile system at Position A is: PEg = 0, KE = ET, Eother = 0. Construct an energy bar graph for the system at Position B (halfway up, 0.025 m above A). Zero level of PEg is Position A; friction and air resistance are negligible.
Click a box to set each bar’s height; click it again to clear the bar to 0. The ET bar is drawn for you.
In 1672, the astronomer Jean Richer carried a pendulum clock that kept accurate time in Paris to Cayenne, near the equator. In Cayenne the clock lost about two and a half minutes each day, which means each swing of its pendulum took slightly longer than in Paris. The length of the pendulum did not change. Today, the acceleration due to gravity is known to be about 9.81 m/s2 in Paris and about 9.78 m/s2 near the equator, because Earth bulges at the equator.
5. Which statement best explains why the clock ran slow in Cayenne?