1. Name and describe Newton's second and third laws of motion. A:
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Newton's Second Law of Motion: This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it is expressed as \( F = m \cdot a \), where \( F \) is the net force applied, \( m \) is the mass of the object, and \( a \) is the acceleration produced.
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Newton's Third Law of Motion: This law states that for every action, there is an equal and opposite reaction. This means that if one object exerts a force on another object, the second object exerts a force of equal magnitude but in the opposite direction on the first object.
2. List examples of each law of motion. A:
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Newton's Second Law Example: Pushing a car (mass) to accelerate it. If you push harder (increased force), the car accelerates faster. Conversely, increasing the car's mass will reduce the acceleration for the same force applied.
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Newton's Third Law Example: When you jump off a small boat, you push down on the boat (action), and in response, the boat pushes you upward (reaction), causing the boat to move backward.
3. Define static friction, and give an example of it. A:
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Static Friction: Static friction is the force that resists the initiation of sliding motion between two surfaces that are in contact and at rest relative to each other. It must be overcome to start moving an object.
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Example of Static Friction: A heavy book resting on a table does not slide until a sufficient horizontal force is applied. The force of static friction prevents it from moving until that threshold is exceeded.
4. Compare and contrast static and kinetic friction. What three concepts does Hooke's Law relate to each other? A:
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Static Friction vs. Kinetic Friction:
- Static Friction: Acts when objects are at rest relative to one another; it can vary up to a maximum value depending on the applied force, opposing the onset of motion.
- Kinetic Friction: Acts when objects are sliding over one another; it is generally less than maximum static friction and remains relatively constant for a given pair of materials.
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Three Concepts of Hooke's Law: Hooke's Law relates the force exerted by a spring (F), the constant of proportionality (k, also known as the spring constant), and the displacement (x) from the spring's equilibrium position. It is expressed as \( F = -k \cdot x \).
5. According to Hooke's Law, in order for a spring to apply a restorative force, what must be true about the displacement of the spring? A:
- According to Hooke's Law, for a spring to apply a restorative force, the spring must be displaced from its equilibrium position. The restorative force is directly proportional to the distance of that displacement. If the spring is not displaced (i.e., at rest), then there is no restorative force applied.
6. Based on Newton's second law of motion, if the force remains constant, what do you need to do in order to decrease the acceleration by half? A:
- To decrease the acceleration by half while keeping the force constant, you need to double the mass of the object. According to Newton's second law \( F = m \cdot a \), if \( F \) is constant and we want \( a \) to be halved, we must increase \( m \).
7. What is the formula to calculate force? A:
- The formula to calculate force is \( F = m \cdot a \), where \( F \) is the force in newtons (N), \( m \) is the mass in kilograms (kg), and \( a \) is the acceleration in meters per second squared (m/s²).
8. Using Newton's Second Law, can you explain why one of the major advancements in spaceflight was the development of strong ceramic (clay) materials to build their rockets out of instead of heavy metals? A:
- The use of strong ceramic materials in rockets allows for a significant reduction in overall mass, which is crucial for achieving the necessary thrust to propel a spacecraft into orbit. According to Newton's Second Law, a lower mass requires less force to achieve the same acceleration. Strong ceramics can provide high strength-to-weight ratios, allowing for structural integrity while minimizing mass (increasing efficiency) and maximizing the thrust-to-weight ratio essential for spaceflight.
9. How do you calculate the acceleration due to gravity on a planet? A:
- The acceleration due to gravity (g) on a planet can be calculated using the formula \( g = \frac{G \cdot M}{r^2} \), where \( G \) is the universal gravitational constant (\( 6.674 \times 10^{-11} , \text{N m}^2/\text{kg}^2 \)), \( M \) is the mass of the planet, and \( r \) is the radius of the planet from its center to the point where the gravity is being measured.
10. How do we know that, according to Newton's Second Law, the force and the acceleration acting on an object are proportional? A:
- According to Newton's Second Law \( F = m \cdot a \), the acceleration \( a \) is found by rearranging the equation to \( a = \frac{F}{m} \). Since mass \( m \) is constant for a given object, any increase in force \( F \) results in a direct proportional increase in acceleration \( a \). Conversely, a decrease in force leads to a decrease in acceleration. This proportional relationship is confirmed through experiments showing that varying force leads to corresponding changes in acceleration.