Question
1.
When you swing on a playground, you are undergoing simple harmonic motion. What is the source of the restoring force?
The spring force
The force of gravity
The normal force
The frictional force
2.
A scale at a grocery store is basically a plate, which is connected to a spring. If you were to toss some vegetables on such a grocery store scale and see that it oscillated with a period of 1.0 second. Assuming a spring constant of 10. N/m, what would the mass of the vegetables be?
3900 grams
390 grams
2500 grams
250 grams
3.
A ball is attached to a vertical spring of 400 N/m spring constant. The ball moves downwards 0.5 meters. What is the mass of the ball?
800 kg
80 kg
200 kg
20 kg
4. What is the wavelength of an F-note played in air (v = 343 m/s)? The frequency of F is 349 Hz.
1.24 m
0.79 m
1.45 m
0.98 m
5.
A wave of amplitude A destructively interferes with a wave of Amplitude B. How would you express their superposition mathematically?
A + B
A / B
A * B
A - B
6. A mass on a horizontal spring is displaced 10 centimeters when pushed with 100 N of force. What is the spring constant?
0.1 N/m
10 N/m
1 N/m
1000 N/m
7. Which statement/s best describes longitudinal waves in air? (Check all that apply)
The air molecules move in the same direction as the wave.
The air molecules do not move.
The air molecules move perpendicular to the direction of the wave.
The air molecules move opposite the direction of the wave
8. A typical motor in a car runs at 5000 revolutions per minute, or cycles per minute. What is the period of oscillations in the average car?
0.0002 s
0.12 s
0.002 s
0.012 s
9. Check any options below that illustrate reflection of a wave at a free boundary.
rope tied to a wall
slinky held at one end
flute
organ pipe
When you swing on a playground, you are undergoing simple harmonic motion. What is the source of the restoring force?
The spring force
The force of gravity
The normal force
The frictional force
2.
A scale at a grocery store is basically a plate, which is connected to a spring. If you were to toss some vegetables on such a grocery store scale and see that it oscillated with a period of 1.0 second. Assuming a spring constant of 10. N/m, what would the mass of the vegetables be?
3900 grams
390 grams
2500 grams
250 grams
3.
A ball is attached to a vertical spring of 400 N/m spring constant. The ball moves downwards 0.5 meters. What is the mass of the ball?
800 kg
80 kg
200 kg
20 kg
4. What is the wavelength of an F-note played in air (v = 343 m/s)? The frequency of F is 349 Hz.
1.24 m
0.79 m
1.45 m
0.98 m
5.
A wave of amplitude A destructively interferes with a wave of Amplitude B. How would you express their superposition mathematically?
A + B
A / B
A * B
A - B
6. A mass on a horizontal spring is displaced 10 centimeters when pushed with 100 N of force. What is the spring constant?
0.1 N/m
10 N/m
1 N/m
1000 N/m
7. Which statement/s best describes longitudinal waves in air? (Check all that apply)
The air molecules move in the same direction as the wave.
The air molecules do not move.
The air molecules move perpendicular to the direction of the wave.
The air molecules move opposite the direction of the wave
8. A typical motor in a car runs at 5000 revolutions per minute, or cycles per minute. What is the period of oscillations in the average car?
0.0002 s
0.12 s
0.002 s
0.012 s
9. Check any options below that illustrate reflection of a wave at a free boundary.
rope tied to a wall
slinky held at one end
flute
organ pipe
Answers
GPT-4o mini
Here are the answers to your questions:
1. **When you swing on a playground, you are undergoing simple harmonic motion. What is the source of the restoring force?**
- **The force of gravity**
2. **A scale at a grocery store is basically a plate, which is connected to a spring. If you were to toss some vegetables on such a grocery store scale and see that it oscillated with a period of 1.0 second. Assuming a spring constant of 10 N/m, what would the mass of the vegetables be?**
- Using the formula for the period of a spring, \( T = 2\pi \sqrt{\frac{m}{k}} \)
- Rearranging gives \( m = \frac{T^2 k}{4\pi^2} = \frac{(1.0)^2 (10)}{4\pi^2} \approx 0.25 \text{ kg} = 250 \text{ grams} \)
- **250 grams**
3. **A ball is attached to a vertical spring of 400 N/m spring constant. The ball moves downwards 0.5 meters. What is the mass of the ball?**
- Using Hooke’s Law: \( F = kx \)
- The force due to the weight of the ball is \( F = mg \), so \( mg = kx \)
- Rearranging gives \( m = \frac{kx}{g} = \frac{400 \times 0.5}{9.81} \approx 20.4 \text{ kg} \)
- **20 kg**
4. **What is the wavelength of an F-note played in air (v = 343 m/s)? The frequency of F is 349 Hz.**
- Using the wave equation: \( v = f \lambda \)
- Rearranging gives \( \lambda = \frac{v}{f} = \frac{343}{349} \approx 0.983 \text{ m} \)
- **0.98 m**
5. **A wave of amplitude A destructively interferes with a wave of Amplitude B. How would you express their superposition mathematically?**
- If they destructively interfere, the mathematical representation would be the difference of the two amplitudes.
- **A - B**
6. **A mass on a horizontal spring is displaced 10 centimeters when pushed with 100 N of force. What is the spring constant?**
- Using Hooke’s Law \( F = kx \)
- Rearranging gives \( k = \frac{F}{x} = \frac{100}{0.1} = 1000 \text{ N/m} \)
- **1000 N/m**
7. **Which statement/s best describes longitudinal waves in air? (Check all that apply)**
- **The air molecules move in the same direction as the wave.**
8. **A typical motor in a car runs at 5000 revolutions per minute, or cycles per minute. What is the period of oscillations in the average car?**
- Period \( T = \frac{1}{\text{frequency}} = \frac{1 \text{ minute}}{5000} = \frac{60 \text{ seconds}}{5000} = 0.012 \text{ s} \)
- **0.012 s**
9. **Check any options below that illustrate reflection of a wave at a free boundary.**
- **slinky held at one end**
- (Rope tied to a wall represents a fixed boundary, while the others are sound instruments and do not demonstrate wave reflection in this context.)
1. **When you swing on a playground, you are undergoing simple harmonic motion. What is the source of the restoring force?**
- **The force of gravity**
2. **A scale at a grocery store is basically a plate, which is connected to a spring. If you were to toss some vegetables on such a grocery store scale and see that it oscillated with a period of 1.0 second. Assuming a spring constant of 10 N/m, what would the mass of the vegetables be?**
- Using the formula for the period of a spring, \( T = 2\pi \sqrt{\frac{m}{k}} \)
- Rearranging gives \( m = \frac{T^2 k}{4\pi^2} = \frac{(1.0)^2 (10)}{4\pi^2} \approx 0.25 \text{ kg} = 250 \text{ grams} \)
- **250 grams**
3. **A ball is attached to a vertical spring of 400 N/m spring constant. The ball moves downwards 0.5 meters. What is the mass of the ball?**
- Using Hooke’s Law: \( F = kx \)
- The force due to the weight of the ball is \( F = mg \), so \( mg = kx \)
- Rearranging gives \( m = \frac{kx}{g} = \frac{400 \times 0.5}{9.81} \approx 20.4 \text{ kg} \)
- **20 kg**
4. **What is the wavelength of an F-note played in air (v = 343 m/s)? The frequency of F is 349 Hz.**
- Using the wave equation: \( v = f \lambda \)
- Rearranging gives \( \lambda = \frac{v}{f} = \frac{343}{349} \approx 0.983 \text{ m} \)
- **0.98 m**
5. **A wave of amplitude A destructively interferes with a wave of Amplitude B. How would you express their superposition mathematically?**
- If they destructively interfere, the mathematical representation would be the difference of the two amplitudes.
- **A - B**
6. **A mass on a horizontal spring is displaced 10 centimeters when pushed with 100 N of force. What is the spring constant?**
- Using Hooke’s Law \( F = kx \)
- Rearranging gives \( k = \frac{F}{x} = \frac{100}{0.1} = 1000 \text{ N/m} \)
- **1000 N/m**
7. **Which statement/s best describes longitudinal waves in air? (Check all that apply)**
- **The air molecules move in the same direction as the wave.**
8. **A typical motor in a car runs at 5000 revolutions per minute, or cycles per minute. What is the period of oscillations in the average car?**
- Period \( T = \frac{1}{\text{frequency}} = \frac{1 \text{ minute}}{5000} = \frac{60 \text{ seconds}}{5000} = 0.012 \text{ s} \)
- **0.012 s**
9. **Check any options below that illustrate reflection of a wave at a free boundary.**
- **slinky held at one end**
- (Rope tied to a wall represents a fixed boundary, while the others are sound instruments and do not demonstrate wave reflection in this context.)