Question
1.Models are particularly useful in relativity and quantum mechanics, where
conditions are outside those normally encountered by humans. What is a model?
2.What determines the validity of a theory?
3.Classical physics is a good approximation to modern physics under certain
circumstances. What are they?
4.When is it necessary to use relativistic quantum mechanics?
5.Can classica physics be used to accurately describe a satellite moving at a speed of
7500 m/s? Expain why or why not.
1.2 Physics quantities andunits
1.The speed limit on some interstate highways is roughly 100 km/h. (a) whatis this in
meters per second? (b) How many miles per hour is this?
2.A car is traveling at a speed of33m/s. (a) whatis its speed in kilometers per hour? (b)
Is it exceeding the speed limit?
3.Suppose that a person has an average heart rate of 72.0 beats/min. How many beats
do they have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?
4.A person’s blood pressure is measured to be120±2mm Hg. What is its percent
uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a
blood pressure measurement of80 mm Hg?
5.A person measures their heart rate by counting the number of beats in30s. If40 ±1
beats are counted in 30.0 ±0.5, what is the heart rate and its uncertainty in beats
per minute?
2.3 Time, velocity and speed
1.Does a car’s odometer measure distance traveled or displacement? Does its
speedometer measure speed or velocity?
2.4 Acceleration
2.Is it possible for velocity to be constant while acceleration is not zero? Explain.
3.If a subway train is moving to the left (has a negative velocity) and then comes to a
stop, what is the direction of its acceleration? Is the acceleration positive or
negative?
2.4 Acceleration: Problem solving
1.A cheetah can accelerate from rest to a speed of 30.0 m/s in 7.00 s. What is its
acceleration?
2.A commuter backs her car out of hergarage with an acceleration of 1.40 m/s2
.
(a)How long does it take her to reach a speed of 2.00 m/s? (b) If she then brakes to a
stop in 0.800 s, what is her deceleration?
conditions are outside those normally encountered by humans. What is a model?
2.What determines the validity of a theory?
3.Classical physics is a good approximation to modern physics under certain
circumstances. What are they?
4.When is it necessary to use relativistic quantum mechanics?
5.Can classica physics be used to accurately describe a satellite moving at a speed of
7500 m/s? Expain why or why not.
1.2 Physics quantities andunits
1.The speed limit on some interstate highways is roughly 100 km/h. (a) whatis this in
meters per second? (b) How many miles per hour is this?
2.A car is traveling at a speed of33m/s. (a) whatis its speed in kilometers per hour? (b)
Is it exceeding the speed limit?
3.Suppose that a person has an average heart rate of 72.0 beats/min. How many beats
do they have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?
4.A person’s blood pressure is measured to be120±2mm Hg. What is its percent
uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a
blood pressure measurement of80 mm Hg?
5.A person measures their heart rate by counting the number of beats in30s. If40 ±1
beats are counted in 30.0 ±0.5, what is the heart rate and its uncertainty in beats
per minute?
2.3 Time, velocity and speed
1.Does a car’s odometer measure distance traveled or displacement? Does its
speedometer measure speed or velocity?
2.4 Acceleration
2.Is it possible for velocity to be constant while acceleration is not zero? Explain.
3.If a subway train is moving to the left (has a negative velocity) and then comes to a
stop, what is the direction of its acceleration? Is the acceleration positive or
negative?
2.4 Acceleration: Problem solving
1.A cheetah can accelerate from rest to a speed of 30.0 m/s in 7.00 s. What is its
acceleration?
2.A commuter backs her car out of hergarage with an acceleration of 1.40 m/s2
.
(a)How long does it take her to reach a speed of 2.00 m/s? (b) If she then brakes to a
stop in 0.800 s, what is her deceleration?
Answers
Answered by
GPT-4o mini
Sure! Let's address your questions one by one:
### 1. What is a model?
A model is a simplified representation of a system, phenomenon, or concept that helps in understanding, predicting, and analyzing its behavior under various conditions. In physics, models are often mathematical formulations that approximate real-world scenarios, allowing scientists to draw conclusions and make predictions about physical behavior, especially in complex situations encountered in relativity and quantum mechanics.
### 2. What determines the validity of a theory?
The validity of a theory is determined by its ability to consistently explain and predict experimental and observational results. Key factors that contribute to its validity include:
- **Empirical Evidence**: The degree to which the theory aligns with experimental results.
- **Falsifiability**: The ability to be tested and potentially disproven by observation or experiment.
- **Consistency**: The internal coherence of the theory and its compatibility with established theories.
- **Simplicity**: Often, more straightforward theories are preferred unless a complex explanation provides significantly better predictions.
### 3. What are the circumstances in which classical physics is a good approximation to modern physics?
Classical physics is a good approximation in circumstances where:
- Speeds are much less than the speed of light (non-relativistic speeds).
- The scales of the systems are large compared to atomic scales (macroscopic scales).
- The effects of quantum mechanics can be neglected, such as in large collections of particles where quantum effects average out.
- Gravitational fields are weak, and time dilation effects are negligible.
### 4. When is it necessary to use relativistic quantum mechanics?
Relativistic quantum mechanics is necessary when:
- The velocities involved approach a significant fraction of the speed of light.
- High-energy quantum systems, such as in particle physics, are considered where relativistic effects play a role.
- The behavior of particles with considerable mass (like electrons in high-energy collisions) is studied, necessitating a consistent incorporation of special relativity with quantum mechanics.
### 5. Can classical physics accurately describe a satellite moving at a speed of 7500 m/s? Explain why or why not.
Classical physics may not accurately describe a satellite moving at a speed of 7500 m/s because this speed is approximately 0.025 times the speed of light (c). While it is not extremely relativistic, relativistic effects (like time dilation and length contraction) begin to become non-negligible at such velocities. Therefore, while classical physics might provide a good approximation, using relativistic physics would yield more precise results.
---
### Physics Quantities and Units
### 1. Convert 100 km/h to meters per second and miles per hour.
**(a)** \( 100 \frac{km}{h} = \frac{100000 m}{3600 s} \approx 27.78 \frac{m}{s} \)
**(b)** \( 100 \frac{km}{h} \approx 62.14 \frac{miles}{h} \) (Using the conversion \( 1 km \approx 0.621371 miles \))
### 2. Speed of a car at 33 m/s.
**(a)** \( 33 \frac{m}{s} = 33 \times 3.6 = 118.8 \frac{km}{h} \)
**(b)** Since the speed limit is 100 km/h, yes, the car of 118.8 km/h is exceeding the speed limit.
### 3. Average heart rate and total beats in 2 years.
**(a)**
\[
72 \frac{beats}{min} \times 60 min/h \times 24 h/d \times 365 d/y \times 2 y = 6758400 \, beats \, (2.0 \text{ y})
\]
**(b)**
\[
72 \frac{beats}{min} \times 60 min/h \times 24 h/d \times 365 d/y \times 2.00 y = 6758400 \, beats
\]
**(c)**
\[
72 \frac{beats}{min} \times 60 min/h \times 24 h/d \times 365 d/y \times 2.000 y = 6758400 \, beats
\]
### 4. Blood pressure measurement uncertainty.
**(a)** Percent uncertainty is given by:
\[
\frac{2}{120} \times 100\% \approx 1.67\%
\]
**(b)** For 80 mm Hg:
\[
1.67\% \times 80 \approx 1.34 \, mmHg
\]
### 5. Heart rate and uncertainty
Given:
- Counts: \( 40 \pm 1 \) beats
- Time: \( 30.0 \pm 0.5 \) seconds
Heart rate (HR):
\[
\text{HR} = \frac{40 \, beats}{30.0 \, s} \times 60 \, s/min = 80 \, beats/min
\]
To find uncertainty in HR, we can use the formula for relative uncertainty:
\[
u_{HR} = HR \left( \frac{u_{count}}{count} + \frac{u_{time}}{time} \right)
\]
Where \( u_{count} = 1 \, beats \) and \( u_{time} = 0.5 \, s \),
\[
u_{HR} = 80 \left( \frac{1}{40} + \frac{0.5}{30} \right) \approx 80 \left( 0.025 + 0.01667 \right) \approx 80 \times 0.04167 \approx 3.33
\]
Thus, the heart rate with uncertainty is:
\[
80 \pm 3.33 \, beats/min
\]
### Time, Velocity, and Speed
### 1. Odometer and speedometer measurements
A car’s odometer measures distance traveled, while its speedometer measures speed (the magnitude of velocity, without considering direction).
### 2. Is it possible for velocity to be constant while acceleration is not zero?
No, if velocity is constant (i.e., unchanging in magnitude and direction), then the acceleration must be zero since acceleration is defined as the rate of change of velocity.
### 3. Direction of acceleration of a subway train
If the subway train is moving to the left with a negative velocity and comes to a stop, its acceleration is directed to the right (positive direction) since it must act in the opposite direction of its motion to reduce its speed to zero.
---
### Acceleration Problem Solving
### 1. Cheetah's acceleration calculation
Given final speed \( v = 30.0 \, m/s \), initial speed \( u = 0 \, m/s \), and time \( t = 7.00 \, s \):
\[
a = \frac{v - u}{t} = \frac{30.0 - 0}{7.00} \approx 4.29 \, m/s^2
\]
### 2. Car acceleration calculations
**(a)** Given an initial speed \( u = 0 \, m/s \), final speed \( v = 2.00 \, m/s \), and acceleration \( a = 1.40 \, m/s^2 \):
\[
t = \frac{v - u}{a} = \frac{2.00 - 0}{1.40} \approx 1.43 \, s
\]
**(b)** If she then brakes to a stop in \( 0.800 \, s \) from \( 2.00 \, m/s \):
Final speed \( v = 0 \, m/s\):
\[
a = \frac{v - u}{t} = \frac{0 - 2.00}{0.800} = -2.5 \, m/s^2 \, (deceleration)
\]
If you have further questions or need clarification on any topic, please let me know!
### 1. What is a model?
A model is a simplified representation of a system, phenomenon, or concept that helps in understanding, predicting, and analyzing its behavior under various conditions. In physics, models are often mathematical formulations that approximate real-world scenarios, allowing scientists to draw conclusions and make predictions about physical behavior, especially in complex situations encountered in relativity and quantum mechanics.
### 2. What determines the validity of a theory?
The validity of a theory is determined by its ability to consistently explain and predict experimental and observational results. Key factors that contribute to its validity include:
- **Empirical Evidence**: The degree to which the theory aligns with experimental results.
- **Falsifiability**: The ability to be tested and potentially disproven by observation or experiment.
- **Consistency**: The internal coherence of the theory and its compatibility with established theories.
- **Simplicity**: Often, more straightforward theories are preferred unless a complex explanation provides significantly better predictions.
### 3. What are the circumstances in which classical physics is a good approximation to modern physics?
Classical physics is a good approximation in circumstances where:
- Speeds are much less than the speed of light (non-relativistic speeds).
- The scales of the systems are large compared to atomic scales (macroscopic scales).
- The effects of quantum mechanics can be neglected, such as in large collections of particles where quantum effects average out.
- Gravitational fields are weak, and time dilation effects are negligible.
### 4. When is it necessary to use relativistic quantum mechanics?
Relativistic quantum mechanics is necessary when:
- The velocities involved approach a significant fraction of the speed of light.
- High-energy quantum systems, such as in particle physics, are considered where relativistic effects play a role.
- The behavior of particles with considerable mass (like electrons in high-energy collisions) is studied, necessitating a consistent incorporation of special relativity with quantum mechanics.
### 5. Can classical physics accurately describe a satellite moving at a speed of 7500 m/s? Explain why or why not.
Classical physics may not accurately describe a satellite moving at a speed of 7500 m/s because this speed is approximately 0.025 times the speed of light (c). While it is not extremely relativistic, relativistic effects (like time dilation and length contraction) begin to become non-negligible at such velocities. Therefore, while classical physics might provide a good approximation, using relativistic physics would yield more precise results.
---
### Physics Quantities and Units
### 1. Convert 100 km/h to meters per second and miles per hour.
**(a)** \( 100 \frac{km}{h} = \frac{100000 m}{3600 s} \approx 27.78 \frac{m}{s} \)
**(b)** \( 100 \frac{km}{h} \approx 62.14 \frac{miles}{h} \) (Using the conversion \( 1 km \approx 0.621371 miles \))
### 2. Speed of a car at 33 m/s.
**(a)** \( 33 \frac{m}{s} = 33 \times 3.6 = 118.8 \frac{km}{h} \)
**(b)** Since the speed limit is 100 km/h, yes, the car of 118.8 km/h is exceeding the speed limit.
### 3. Average heart rate and total beats in 2 years.
**(a)**
\[
72 \frac{beats}{min} \times 60 min/h \times 24 h/d \times 365 d/y \times 2 y = 6758400 \, beats \, (2.0 \text{ y})
\]
**(b)**
\[
72 \frac{beats}{min} \times 60 min/h \times 24 h/d \times 365 d/y \times 2.00 y = 6758400 \, beats
\]
**(c)**
\[
72 \frac{beats}{min} \times 60 min/h \times 24 h/d \times 365 d/y \times 2.000 y = 6758400 \, beats
\]
### 4. Blood pressure measurement uncertainty.
**(a)** Percent uncertainty is given by:
\[
\frac{2}{120} \times 100\% \approx 1.67\%
\]
**(b)** For 80 mm Hg:
\[
1.67\% \times 80 \approx 1.34 \, mmHg
\]
### 5. Heart rate and uncertainty
Given:
- Counts: \( 40 \pm 1 \) beats
- Time: \( 30.0 \pm 0.5 \) seconds
Heart rate (HR):
\[
\text{HR} = \frac{40 \, beats}{30.0 \, s} \times 60 \, s/min = 80 \, beats/min
\]
To find uncertainty in HR, we can use the formula for relative uncertainty:
\[
u_{HR} = HR \left( \frac{u_{count}}{count} + \frac{u_{time}}{time} \right)
\]
Where \( u_{count} = 1 \, beats \) and \( u_{time} = 0.5 \, s \),
\[
u_{HR} = 80 \left( \frac{1}{40} + \frac{0.5}{30} \right) \approx 80 \left( 0.025 + 0.01667 \right) \approx 80 \times 0.04167 \approx 3.33
\]
Thus, the heart rate with uncertainty is:
\[
80 \pm 3.33 \, beats/min
\]
### Time, Velocity, and Speed
### 1. Odometer and speedometer measurements
A car’s odometer measures distance traveled, while its speedometer measures speed (the magnitude of velocity, without considering direction).
### 2. Is it possible for velocity to be constant while acceleration is not zero?
No, if velocity is constant (i.e., unchanging in magnitude and direction), then the acceleration must be zero since acceleration is defined as the rate of change of velocity.
### 3. Direction of acceleration of a subway train
If the subway train is moving to the left with a negative velocity and comes to a stop, its acceleration is directed to the right (positive direction) since it must act in the opposite direction of its motion to reduce its speed to zero.
---
### Acceleration Problem Solving
### 1. Cheetah's acceleration calculation
Given final speed \( v = 30.0 \, m/s \), initial speed \( u = 0 \, m/s \), and time \( t = 7.00 \, s \):
\[
a = \frac{v - u}{t} = \frac{30.0 - 0}{7.00} \approx 4.29 \, m/s^2
\]
### 2. Car acceleration calculations
**(a)** Given an initial speed \( u = 0 \, m/s \), final speed \( v = 2.00 \, m/s \), and acceleration \( a = 1.40 \, m/s^2 \):
\[
t = \frac{v - u}{a} = \frac{2.00 - 0}{1.40} \approx 1.43 \, s
\]
**(b)** If she then brakes to a stop in \( 0.800 \, s \) from \( 2.00 \, m/s \):
Final speed \( v = 0 \, m/s\):
\[
a = \frac{v - u}{t} = \frac{0 - 2.00}{0.800} = -2.5 \, m/s^2 \, (deceleration)
\]
If you have further questions or need clarification on any topic, please let me know!
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