Podcast
Questions and Answers
Which of the following is a scalar quantity?
Which of the following is a scalar quantity?
- Time (correct)
- Acceleration
- Force
- Velocity
A jogger runs 40 meters North, then 30 meters East. What is the magnitude of the jogger's displacement?
A jogger runs 40 meters North, then 30 meters East. What is the magnitude of the jogger's displacement?
- 70 meters
- 10 meters
- 50 meters (correct)
- 120 meters
A car travels 60 kilometers in 2 hours and then covers 30 kilometers in 8 hours. What is the average speed of the car?
A car travels 60 kilometers in 2 hours and then covers 30 kilometers in 8 hours. What is the average speed of the car?
- 30 km/h
- 60 km/h
- 9 km/h (correct)
- 45 km/h
A particle's position along the x-axis is given by $x = 7.8 + 9.2t - 2.1t^3$, where x is in meters and t is in seconds. Is the velocity of the particle constant?
A particle's position along the x-axis is given by $x = 7.8 + 9.2t - 2.1t^3$, where x is in meters and t is in seconds. Is the velocity of the particle constant?
Which of the following scenarios involves acceleration?
Which of the following scenarios involves acceleration?
A car starts from rest and accelerates to a velocity of 25 m/s in 5 minutes. What is the average acceleration of the car?
A car starts from rest and accelerates to a velocity of 25 m/s in 5 minutes. What is the average acceleration of the car?
A tennis ball is thrown straight up with an initial speed of 22.5 m/s and is caught at the same distance above the ground from where it was thrown. What is the time the ball remains in the air, neglecting air resistance?
A tennis ball is thrown straight up with an initial speed of 22.5 m/s and is caught at the same distance above the ground from where it was thrown. What is the time the ball remains in the air, neglecting air resistance?
A racer accelerates from rest at a constant rate of 3.0 m/s². Assuming constant acceleration, how far has the racer traveled by the end of 13 seconds?
A racer accelerates from rest at a constant rate of 3.0 m/s². Assuming constant acceleration, how far has the racer traveled by the end of 13 seconds?
A rocket accelerates uniformly from rest to a speed of 25 m/s after it has traveled 75 m. What is the rocket's acceleration?
A rocket accelerates uniformly from rest to a speed of 25 m/s after it has traveled 75 m. What is the rocket's acceleration?
Which of the following is true about free fall?
Which of the following is true about free fall?
In a vacuum, which of the following would fall at the same rate?
In a vacuum, which of the following would fall at the same rate?
A ball is thrown horizontally from a height of 6 meters with an initial speed of 30 m/s. Approximately how long will it take the ball to reach the ground, if air resistance is negligible?
A ball is thrown horizontally from a height of 6 meters with an initial speed of 30 m/s. Approximately how long will it take the ball to reach the ground, if air resistance is negligible?
A ball is thrown horizontally from a height of 6 meters with an initial speed of 30 m/s. Approximately how far will the ball travel horizontally before hitting the ground, assuming air resistance is negligible?
A ball is thrown horizontally from a height of 6 meters with an initial speed of 30 m/s. Approximately how far will the ball travel horizontally before hitting the ground, assuming air resistance is negligible?
An object is launched at a velocity of 20 m/s at an angle of 25° upward with the horizontal. What is the maximum height reached by the object, neglecting air resistance?
An object is launched at a velocity of 20 m/s at an angle of 25° upward with the horizontal. What is the maximum height reached by the object, neglecting air resistance?
Which of the following is the correct definition of force?
Which of the following is the correct definition of force?
What are the four fundamental forces in nature?
What are the four fundamental forces in nature?
A rocket launching into space is an example of which of Newton's Laws of Motion?
A rocket launching into space is an example of which of Newton's Laws of Motion?
A person swimming in a pool is an example of which of Newton's Laws of Motion?
A person swimming in a pool is an example of which of Newton's Laws of Motion?
Why does a person thrown from a moving car continue to move forward, even after leaving the car?
Why does a person thrown from a moving car continue to move forward, even after leaving the car?
What is the relationship between mass and weight?
What is the relationship between mass and weight?
A box with a mass of 20 kg is at rest on a cement floor. The coefficient of static friction between the box and the floor is 0.25. What is the minimum horizontal force required to start moving the box?
A box with a mass of 20 kg is at rest on a cement floor. The coefficient of static friction between the box and the floor is 0.25. What is the minimum horizontal force required to start moving the box?
What is the main difference between static and kinetic friction?
What is the main difference between static and kinetic friction?
Which of the following statements about friction is correct?
Which of the following statements about friction is correct?
If a moving object experiences friction, what happens to its kinetic energy?
If a moving object experiences friction, what happens to its kinetic energy?
If two vectors A and B are perpendicular to each other, what is their dot product?
If two vectors A and B are perpendicular to each other, what is their dot product?
What does the dot product of two vectors intuitively tell us?
What does the dot product of two vectors intuitively tell us?
Two vectors A and B are perpendicular to each other, with magnitudes |A| = 2.5N and |B| = 3.0N. If the angle between them is changed to 30 degrees, what is the new cross product?
Two vectors A and B are perpendicular to each other, with magnitudes |A| = 2.5N and |B| = 3.0N. If the angle between them is changed to 30 degrees, what is the new cross product?
How does increasing the launch angle (relative to the horizontal) generally affect the peak height and range of a projectile, assuming all other factors remain constant?
How does increasing the launch angle (relative to the horizontal) generally affect the peak height and range of a projectile, assuming all other factors remain constant?
In projectile motion, what happens to the vertical component of velocity at the highest point of the trajectory (assuming no air resistance)?
In projectile motion, what happens to the vertical component of velocity at the highest point of the trajectory (assuming no air resistance)?
A pirate ship is 560 m from a military island base. A cannon fires balls with vo = 82 m/s. At what horizontal angle must a ball be fired to hit the ship?
A pirate ship is 560 m from a military island base. A cannon fires balls with vo = 82 m/s. At what horizontal angle must a ball be fired to hit the ship?
Calculate the exact cross product of vector a (3i - 3j + k) and vector b (5i + 6j + 8k)
Calculate the exact cross product of vector a (3i - 3j + k) and vector b (5i + 6j + 8k)
A particle moves such that its position on the x-axis is defined by $x = t^3 -27t + 4$. Determine the acceleration of the particle at t = 3 seconds.
A particle moves such that its position on the x-axis is defined by $x = t^3 -27t + 4$. Determine the acceleration of the particle at t = 3 seconds.
Which of the following quantities is a vector?
Which of the following quantities is a vector?
Which of the following is an example of calculating displacement?
Which of the following is an example of calculating displacement?
A student walks 50 meters east, then 20 meters north, and finally 10 meters west. What is the approximate direction of the student's resultant displacement from the original point?
A student walks 50 meters east, then 20 meters north, and finally 10 meters west. What is the approximate direction of the student's resultant displacement from the original point?
What is the primary difference between speed and velocity?
What is the primary difference between speed and velocity?
An athlete runs 100 meters east and then 50 meters west in 50 seconds. What is the athlete's average velocity?
An athlete runs 100 meters east and then 50 meters west in 50 seconds. What is the athlete's average velocity?
Under what condition might an object have a changing velocity, but constant speed?
Under what condition might an object have a changing velocity, but constant speed?
The position of a particle is given by the equation $x(t) = 3t^2 - 2t + 1$, where $x$ is in meters and $t$ is in seconds. What is the particle's velocity at $t = 2$ seconds?
The position of a particle is given by the equation $x(t) = 3t^2 - 2t + 1$, where $x$ is in meters and $t$ is in seconds. What is the particle's velocity at $t = 2$ seconds?
Which of the following scenarios represents a situation with non-zero acceleration?
Which of the following scenarios represents a situation with non-zero acceleration?
A race car accelerates from 20 m/s to 30 m/s in 5 seconds. What is the magnitude of its average acceleration?
A race car accelerates from 20 m/s to 30 m/s in 5 seconds. What is the magnitude of its average acceleration?
A ball is thrown upwards with an initial velocity of 15 m/s. Assuming negligible air resistance, what is its velocity at the highest point of its trajectory?
A ball is thrown upwards with an initial velocity of 15 m/s. Assuming negligible air resistance, what is its velocity at the highest point of its trajectory?
A rock is dropped from a bridge. If it takes 3 seconds to hit the water, approximately how high is the bridge? (Assume g = 9.8 m/s² and neglect air resistance)
A rock is dropped from a bridge. If it takes 3 seconds to hit the water, approximately how high is the bridge? (Assume g = 9.8 m/s² and neglect air resistance)
A projectile is launched at an angle of 30° above the horizontal with an initial velocity of 40 m/s. What is the initial vertical component of the velocity?
A projectile is launched at an angle of 30° above the horizontal with an initial velocity of 40 m/s. What is the initial vertical component of the velocity?
In projectile motion, what remains constant (neglecting air resistance)?
In projectile motion, what remains constant (neglecting air resistance)?
Which of the following best describes the term 'force'?
Which of the following best describes the term 'force'?
Which of the following fundamental forces is responsible for holding the nucleus of an atom together?
Which of the following fundamental forces is responsible for holding the nucleus of an atom together?
A stationary object remains at rest unless acted upon by a net force. Which of Newton's Laws describes this concept?
A stationary object remains at rest unless acted upon by a net force. Which of Newton's Laws describes this concept?
A book rests on a table. According to Newton's Third Law, what is the reaction force to the force of the book on the table?
A book rests on a table. According to Newton's Third Law, what is the reaction force to the force of the book on the table?
Why does an astronaut in space float inside the International Space Station?
Why does an astronaut in space float inside the International Space Station?
An object's weight is MOST directly related to which of the following?
An object's weight is MOST directly related to which of the following?
A 50 kg crate is at rest on a horizontal floor. If the coefficient of static friction between the crate and the floor is 0.4, what is the minimum horizontal force required to START moving the crate?
A 50 kg crate is at rest on a horizontal floor. If the coefficient of static friction between the crate and the floor is 0.4, what is the minimum horizontal force required to START moving the crate?
How does kinetic friction typically compare to static friction for the same two surfaces?
How does kinetic friction typically compare to static friction for the same two surfaces?
Which of the following factors does NOT influence the force of friction between two solid surfaces?
Which of the following factors does NOT influence the force of friction between two solid surfaces?
What happens to the energy 'lost' due to friction when a box slides across a rough surface?
What happens to the energy 'lost' due to friction when a box slides across a rough surface?
Vectors A and B have magnitudes of 5 and 8, respectively. If the angle between them is 90 degrees, what is the approximate magnitude of their resultant vector when they are added?
Vectors A and B have magnitudes of 5 and 8, respectively. If the angle between them is 90 degrees, what is the approximate magnitude of their resultant vector when they are added?
If two vectors are anti-parallel (pointing in exactly opposite directions), what is true of their dot product?
If two vectors are anti-parallel (pointing in exactly opposite directions), what is true of their dot product?
What is the cross product of two parallel vectors?
What is the cross product of two parallel vectors?
A projectile is launched at an angle of 45 degrees. What single adjustment could maximize its range, assuming initial speed and launch location remain unchanged?
A projectile is launched at an angle of 45 degrees. What single adjustment could maximize its range, assuming initial speed and launch location remain unchanged?
What is the effect of air resistance on the range of a projectile?
What is the effect of air resistance on the range of a projectile?
A cannonball is fired with an initial velocity of 100 m/s at an angle $\theta$ above the horizontal. If the horizontal range of the cannonball is 500 m, which equation is most appropriate to approximate the launch angle?
A cannonball is fired with an initial velocity of 100 m/s at an angle $\theta$ above the horizontal. If the horizontal range of the cannonball is 500 m, which equation is most appropriate to approximate the launch angle?
Given vector $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$ and vector $\vec{b} = \hat{i} + \hat{j} - 2\hat{k}$, what is the z-component of the cross product $\vec{a} \times \vec{b}$?
Given vector $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$ and vector $\vec{b} = \hat{i} + \hat{j} - 2\hat{k}$, what is the z-component of the cross product $\vec{a} \times \vec{b}$?
A particle's position is given by $x(t) = t^3 - 6t^2 + 9t$, where x is in meters and t is in seconds. At what time(s) is the velocity of the particle equal to zero?
A particle's position is given by $x(t) = t^3 - 6t^2 + 9t$, where x is in meters and t is in seconds. At what time(s) is the velocity of the particle equal to zero?
A car is moving in a straight line with an initial velocity $v_0$. It accelerates with a constant acceleration $a$ for a time $t$. Which of the following expressions represents the final velocity $v$ of the car?
A car is moving in a straight line with an initial velocity $v_0$. It accelerates with a constant acceleration $a$ for a time $t$. Which of the following expressions represents the final velocity $v$ of the car?
A ball is thrown straight upwards and returns to its starting point. Assuming negligible air resistance, what is the ball's total displacement?
A ball is thrown straight upwards and returns to its starting point. Assuming negligible air resistance, what is the ball's total displacement?
A car travels at a constant velocity of 20 m/s for 10 seconds. What is the distance covered by the car?
A car travels at a constant velocity of 20 m/s for 10 seconds. What is the distance covered by the car?
Which of the following is a valid unit for measuring acceleration?
Which of the following is a valid unit for measuring acceleration?
If an object has a constant, non-zero acceleration, which of the following must be true?
If an object has a constant, non-zero acceleration, which of the following must be true?
An object is thrown upwards with an initial velocity $v_0$ from a height $h_0$. What equation describes its height $h(t)$ at time $t$, assuming constant gravitational acceleration $g$ downwards?
An object is thrown upwards with an initial velocity $v_0$ from a height $h_0$. What equation describes its height $h(t)$ at time $t$, assuming constant gravitational acceleration $g$ downwards?
Two cars are moving in the same direction on a straight road. Car A is moving at 30 m/s and Car B is moving at 20 m/s. What is the relative velocity of Car A with respect to Car B?
Two cars are moving in the same direction on a straight road. Car A is moving at 30 m/s and Car B is moving at 20 m/s. What is the relative velocity of Car A with respect to Car B?
A train starts from rest and accelerates uniformly at a rate of 0.5 m/s². How long does it take for the train to reach a speed of 36 km/h?
A train starts from rest and accelerates uniformly at a rate of 0.5 m/s². How long does it take for the train to reach a speed of 36 km/h?
Suppose that two vectors, $\vec{A}$ and $\vec{B}$ are defined such that $\vec{A} \cdot \vec{B} = -|A||B|$. What is the angle between vectors $\vec{A}$ and $\vec{B}$?
Suppose that two vectors, $\vec{A}$ and $\vec{B}$ are defined such that $\vec{A} \cdot \vec{B} = -|A||B|$. What is the angle between vectors $\vec{A}$ and $\vec{B}$?
Flashcards
What are scalars?
What are scalars?
Quantities with magnitude only.
What are vectors?
What are vectors?
Quantities with both magnitude and direction.
What is component method?
What is component method?
Breaking vectors into horizontal and vertical parts.
What is the dot product?
What is the dot product?
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What is the cross product?
What is the cross product?
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What is motion?
What is motion?
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What is kinematics?
What is kinematics?
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What is dynamics?
What is dynamics?
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What is distance?
What is distance?
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What is displacement?
What is displacement?
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What is speed?
What is speed?
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What is velocity?
What is velocity?
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What is acceleration?
What is acceleration?
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What is Uniform Accelerated Motion?
What is Uniform Accelerated Motion?
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What is free fall?
What is free fall?
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What is Projectile Motion?
What is Projectile Motion?
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What is force?
What is force?
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Force
Force
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What is Gravity, Electromagnetism, Strong and Weak forces.
What is Gravity, Electromagnetism, Strong and Weak forces.
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What is Newton's First Law?
What is Newton's First Law?
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What is Newton's Second Law?
What is Newton's Second Law?
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What is Newton's Third Law?
What is Newton's Third Law?
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What is mass?
What is mass?
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What is weight?
What is weight?
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What is Friction?
What is Friction?
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What is Static Friction
What is Static Friction
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What is Kinetic Friction?
What is Kinetic Friction?
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Direction of a Vector
Direction of a Vector
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Component Method steps
Component Method steps
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Average Speed
Average Speed
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Average Velocity
Average Velocity
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Define: Acceleration
Define: Acceleration
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What affects free fall?
What affects free fall?
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Projectile Max Height
Projectile Max Height
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Projectile Max Range
Projectile Max Range
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Friction proportional to?
Friction proportional to?
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Friction and surface?
Friction and surface?
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Friction area of contact?
Friction area of contact?
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What causes Static CoF?
What causes Static CoF?
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What causes Kinetic CoF?
What causes Kinetic CoF?
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Study Notes
Newtonian Mechanics
- Newtonian mechanics is the study of motion, forces, and their interactions
Goals for the day
- Vectors and scalars are two different types of quantities, one having magnitude and direction, the other having magnitude only.
- Distance and displacement distinguish the total length of a path versus the shortest length from start to finish.
- Speed, velocity, and acceleration relate to how fast an object is moving, its rate of change in position with direction, and its rate of change in velocity, respectively.
- Uniform motion refers to movement at a constant velocity.
- Projectile motion is the curved path an object follows when thrown or launched.
- The laws of motion are fundamental principles governing how objects move or remain at rest when forces are applied.
- Friction is a force that opposes motion between surfaces in contact.
Scalars vs Vectors
- Scalars are quantities that have magnitude only (e.g., speed, mass, pressure, temperature, time, and volume).
- Vectors are quantities that have both magnitude and direction (e.g., velocity, weight, friction).
- For example, A is 50 N of E, B is 45 N of W, C is 20 S of E, and D is N, specifying directions of vectors.
Component Method
- The component method is used to add two or more vectors
- Resolve vectors into horizontal and vertical components, which depend on the quadrant.
- Find the algebraic sum of all horizontal and vertical components. The sums represent the resultant's horizontal and vertical components.
- The Pythagorean theorem can be used to calculate the magnitude of the resultant since the vertical and horizontal components are perpendicular.
- Determine the quadrant of the resultant based on the sums' signs, which gives the resultant's direction.
- Solve for the angle the resultant makes with the horizontal.
- For the jogger problem: a jogger runs 4.00m 50 N of E, 5m west, 6.00 30 S of W, 10m north. Find the resultant displacement from where he started
- Horizontal components consist of + 4m cos50 for 4.00m 50 N of E , −5m for 5m west, and −6m cos 60 for 6.00 30 S of W
- Vertical components consist of + 4m sin50 for 4.00m 50 N of E and −6m sin60 for 6.00 30 S of W, +10m for 10m north
Dot Product
- The dot product is a way to combine two vectors, indicating how much they point in the same direction.
- For vectors a and b, the dot product is calculated as: a⋅b = |a| x |b| x cos(θ), where |a| and |b| are the magnitudes (lengths) of vectors a and b, and θ is the angle between a and b.
- Sample Problem
- For two perpendicular vectors A and B, the dot product is 0, since their dot product = (2.5N)(3.0N)cos90 = 0
- When the angle of two vectors is 30, then their dot product = (2.5N)(3.0N)cos30 = 6.50 N -Given A = <1,2> B = <3,4>, their dot product is expressed as [(1)(3) + (2)(4)] = 9, leading to angle between these vectors being equal to 50.98 degrees
Cross Product
- The cross product yields a vector product whose direction follows the right-hand rule.
- For two vectors a and b, the formula is a x b = |a| |b| sin(θ) n
- |a| and |b| represent the magnitudes (lengths) of vectors a and b.
- θ is the angle between a and b.
- n is the unit vector at right angles to both a and b. -Sample Problem
- If two vectors, A and B, are perpendicular, then their cross product equal to (2.5N)(3.0N)sin90 = 7.5N
- When the angle is 30, their new cross product is (2.5N)(3.0N)sin30 = 3.75N
- If A = <1,3,4> or (A = i + 3j + 4k)and B = <2,7, -5> or (B = 2i +7j -5k), then (-15-28)i + (-5 -8)k + (7-6)k or i – 13k +k
What is Motion?
- Motion is the action or process of moving or changing position
- Kinematics studies how objects move by quantitatively describing it without regard to physical reasons
- Dynamics focus on why objects move, studying forces and motion's relationships.
Displacement vs. Distance
- Distance is a scalar quantity. If a body moves from a point 'A' to point 'D', the total path length ('ABCD') is the distance the body moved.
- Displacement is a vector quantity. It's the actual distance moved by a body from 'A' toward 'D' in a straight line.
- Using Pythagorean theorem with sides that are 30m + 40m , produces a resultant of 50m in displacement
Speed and Velocity
- Speed is the scalar quantity indicating only the magnitude or rate of change of an object.
- Velocity is the vector quantity signifying the magnitude and direction of an object's movement.
Acceleration
- Acceleration is the rate of change of velocity and can involve changes in speed (increase or decrease) and/or direction.
Uniform Accelerated Motion
- During uniform accelerated motion, acceleration is roughly constant, in which five equations describe the motion of a particle
- Five variables found in equations that are part of accelerated motion: Δd, Δt, v₀, v, and aav
Free Fall
- Free fall is when an object moves under gravitational force alone.
- Free fall doesn’t necessarily mean the object is falling down only.
- Objects thrown upward or downward and released from rest are examples of free fall.
- The constant acceleration of a freely falling body is the acceleration due to gravity.
Projectile Motion
- Projectile motion involves an object thrown in the air that follows a curved path.
- Hmax =v₀² sin² α= maximum height that a projectile can reach will be possible with a degree of 90.
- The maximum height decreases as the launch angle decreases due to reduced vertical launch speed.
- Range - R is the horizontal range (distance) =v₀² sin 2α/g. The maximum range is reached with a launch angle 45 deg.
Forces
- Force is an influence that can change object's motion.
- Applying force to object results in velocity and acceleration.
- A force is measured in the SI unit Newton and has vector properties
Newton's Laws of Motion
- 1st Law: A body in motion/ at rest remains in motion/at rest unless acted upon by a force.
- 2nd Law: Force equals mass times acceleration, expressed as: F = m*a
- 3rd Law: For every action, there is an equal and opposite reaction.
Mass and Weight
- Mass量 -Measure of the inertia of the body; quantity of matter (scalar)
- Weight重量 -Force with which the body is attracted toward Earth; vector
Friction
- Friction is a force that opposes the direction of motion of one object opposing another.
- Static CoF: Break static friction to start motion.
- Kinetic CoF: Keep an object in motion
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