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Two coccal bacteria, each with a mass of $9.5 \times 10^{-16}$ kg, are separated by a distance of $1 \mu m$. What is the gravitational force between them, given $G = 6.67 \times 10^{-11} Nm^2/kg^2$?
Two coccal bacteria, each with a mass of $9.5 \times 10^{-16}$ kg, are separated by a distance of $1 \mu m$. What is the gravitational force between them, given $G = 6.67 \times 10^{-11} Nm^2/kg^2$?
If the radius of a planet is doubled, how does the free fall acceleration ($g$) at the surface change, assuming the planet's mass remains constant?
If the radius of a planet is doubled, how does the free fall acceleration ($g$) at the surface change, assuming the planet's mass remains constant?
A sphere with a mass of 20 kg is placed on the Earth's surface where $g = 9.8 m/s^2$. What is the weight of the sphere?
A sphere with a mass of 20 kg is placed on the Earth's surface where $g = 9.8 m/s^2$. What is the weight of the sphere?
A box rests on a horizontal surface. A force of 15 N is applied upwards, while gravity exerts a force of 11 N downwards on the box. What is the normal force exerted by the surface on the box?
A box rests on a horizontal surface. A force of 15 N is applied upwards, while gravity exerts a force of 11 N downwards on the box. What is the normal force exerted by the surface on the box?
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Which of the following best describes the direction of the normal force exerted by a surface on an object?
Which of the following best describes the direction of the normal force exerted by a surface on an object?
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What primarily causes the force of friction between two surfaces in contact?
What primarily causes the force of friction between two surfaces in contact?
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What is the primary role of static friction?
What is the primary role of static friction?
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An object is placed on a slope. As the angle of the slope increases, how does the magnitude of the normal force acting on the object change?
An object is placed on a slope. As the angle of the slope increases, how does the magnitude of the normal force acting on the object change?
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Which statement accurately describes the difference between scalar and vector quantities?
Which statement accurately describes the difference between scalar and vector quantities?
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A force vector is represented by $\vec{F}$. Which of the following represents the magnitude of this vector?
A force vector is represented by $\vec{F}$. Which of the following represents the magnitude of this vector?
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What does the negative of a vector represent?
What does the negative of a vector represent?
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Two displacement vectors, one 5m and the other 3m, are acting along the same line. If they point in the same direction, what is the magnitude of the resultant vector?
Two displacement vectors, one 5m and the other 3m, are acting along the same line. If they point in the same direction, what is the magnitude of the resultant vector?
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When resolving a vector into its components, what information do the components provide?
When resolving a vector into its components, what information do the components provide?
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What is the significance of the algebraic sign ( + or − ) of a vector component?
What is the significance of the algebraic sign ( + or − ) of a vector component?
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Which of the following is a false statement about vector magnitudes?
Which of the following is a false statement about vector magnitudes?
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If two vectors of magnitudes 3N and 4N are added, what is the minimum magnitude of the resultant vector?
If two vectors of magnitudes 3N and 4N are added, what is the minimum magnitude of the resultant vector?
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A car travels 5 km east, then 3 km south, and finally 2 km west. What is the magnitude and direction of the car's resultant displacement?
A car travels 5 km east, then 3 km south, and finally 2 km west. What is the magnitude and direction of the car's resultant displacement?
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A hiker travels 100 m north and then 50 m east. What is the magnitude and direction of the hiker's displacement?
A hiker travels 100 m north and then 50 m east. What is the magnitude and direction of the hiker's displacement?
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Which of the following is NOT a fundamental force?
Which of the following is NOT a fundamental force?
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What determines an object's motion when multiple forces act upon it?
What determines an object's motion when multiple forces act upon it?
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An object experiences two forces: 10N to the right and 4N to the left. What is the net force acting on the object?
An object experiences two forces: 10N to the right and 4N to the left. What is the net force acting on the object?
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According to Newton's First Law, what condition must be met for an object's velocity to remain constant?
According to Newton's First Law, what condition must be met for an object's velocity to remain constant?
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Which of the following best exemplifies inertia?
Which of the following best exemplifies inertia?
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A force vector has a magnitude of 15 N and is directed 30° above the +x-axis. What is the magnitude of its y-component?
A force vector has a magnitude of 15 N and is directed 30° above the +x-axis. What is the magnitude of its y-component?
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In a free-body diagram, which forces should be included?
In a free-body diagram, which forces should be included?
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A displacement vector has an x-component of -5.0 m and a y-component of +8.0 m. In which quadrant does this vector lie?
A displacement vector has an x-component of -5.0 m and a y-component of +8.0 m. In which quadrant does this vector lie?
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Given a vector with a magnitude of 20 units and an angle of 60° with respect to the x-axis, what are the approximate magnitudes of its x and y components?
Given a vector with a magnitude of 20 units and an angle of 60° with respect to the x-axis, what are the approximate magnitudes of its x and y components?
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Vector A has components $A_x = -3$ and $A_y = 4$. What is the angle of this vector with respect to the positive x-axis?
Vector A has components $A_x = -3$ and $A_y = 4$. What is the angle of this vector with respect to the positive x-axis?
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Which trigonometric function is defined as the ratio of the opposite side to the hypotenuse in a right triangle?
Which trigonometric function is defined as the ratio of the opposite side to the hypotenuse in a right triangle?
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A vector has a negative x-component and a negative y-component. In which quadrant does this vector lie?
A vector has a negative x-component and a negative y-component. In which quadrant does this vector lie?
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Vector A has a magnitude of 10 and makes an angle of 30 degrees with the positive x-axis. Vector B has a magnitude of 15 and makes an angle of 120 degrees with the positive x-axis. What is the x-component of the resultant vector A + B?
Vector A has a magnitude of 10 and makes an angle of 30 degrees with the positive x-axis. Vector B has a magnitude of 15 and makes an angle of 120 degrees with the positive x-axis. What is the x-component of the resultant vector A + B?
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A projectile is launched with an initial velocity $v_0$ at an angle $\theta$ with respect to the horizontal. Assuming negligible air resistance, what is the y-component of the projectile's velocity at the highest point of its trajectory?
A projectile is launched with an initial velocity $v_0$ at an angle $\theta$ with respect to the horizontal. Assuming negligible air resistance, what is the y-component of the projectile's velocity at the highest point of its trajectory?
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When adding vectors $\vec{A}$ and $\vec{B}$ to obtain $\vec{C}$, which of the following statements is always true?
When adding vectors $\vec{A}$ and $\vec{B}$ to obtain $\vec{C}$, which of the following statements is always true?
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In a scenario where multiple forces are acting on an object, what is the purpose of creating a free-body diagram?
In a scenario where multiple forces are acting on an object, what is the purpose of creating a free-body diagram?
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A force $\vec{F_1}$ of 30 N acts on an object at an angle of 30° above the +x axis, and a force $\vec{F_2}$ of 40 N acts on the same object along the +y axis. What is the approximate magnitude of the resultant force?
A force $\vec{F_1}$ of 30 N acts on an object at an angle of 30° above the +x axis, and a force $\vec{F_2}$ of 40 N acts on the same object along the +y axis. What is the approximate magnitude of the resultant force?
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In the context of vector addition, what does 'resolving a force into components' mean?
In the context of vector addition, what does 'resolving a force into components' mean?
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Consider three forces acting on an object: $\vec{F_1} = 20\hat{i}$ N, $\vec{F_2} = -10\hat{j}$ N, and $\vec{F_3} = -5\hat{i} + 5\hat{j}$ N. What is the x-component of the resultant force?
Consider three forces acting on an object: $\vec{F_1} = 20\hat{i}$ N, $\vec{F_2} = -10\hat{j}$ N, and $\vec{F_3} = -5\hat{i} + 5\hat{j}$ N. What is the x-component of the resultant force?
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An object has two forces acting on it: 50 N at 0 degrees and 30 N at 90 degrees. What is the approximate angle of the resultant force with respect to the x-axis?
An object has two forces acting on it: 50 N at 0 degrees and 30 N at 90 degrees. What is the approximate angle of the resultant force with respect to the x-axis?
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A person is pulling a box with a force of 100 N at an angle of 60 degrees above the horizontal. What is the horizontal component of the force?
A person is pulling a box with a force of 100 N at an angle of 60 degrees above the horizontal. What is the horizontal component of the force?
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When should you exclude a force from a free-body diagram?
When should you exclude a force from a free-body diagram?
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Two spheres, each with a mass of 30 kg, are separated by a center-to-center distance of 0.05 m. Which of the following best approximates the gravitational force between them?
Two spheres, each with a mass of 30 kg, are separated by a center-to-center distance of 0.05 m. Which of the following best approximates the gravitational force between them?
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A radio transmitter's power output is changed such that the new power, $P$, is four times the initial power, $P_0$. By what factor has the power increased?
A radio transmitter's power output is changed such that the new power, $P$, is four times the initial power, $P_0$. By what factor has the power increased?
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If the kinetic energy of an object increases by 25%, by what factor is the new kinetic energy, $E_f$, related to the original kinetic energy, $E_0$?
If the kinetic energy of an object increases by 25%, by what factor is the new kinetic energy, $E_f$, related to the original kinetic energy, $E_0$?
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The speed of a car decreases by 10% after the driver applies the brakes. If the initial speed was $v_0$, what is the final speed, $v_f$, in terms of $v_0$?
The speed of a car decreases by 10% after the driver applies the brakes. If the initial speed was $v_0$, what is the final speed, $v_f$, in terms of $v_0$?
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An object's momentum increases by 300%. By what factor has its momentum increased?
An object's momentum increases by 300%. By what factor has its momentum increased?
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A scientist measures the length of a bacterium under a microscope and finds its length has decreased by 5%. If the original length was $L_0$, what is the new length, $L_f$?
A scientist measures the length of a bacterium under a microscope and finds its length has decreased by 5%. If the original length was $L_0$, what is the new length, $L_f$?
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The population of a town increases by 8% in one year. If the initial population was $P_0$, what is the final population, $P_f$, at the end of the year?
The population of a town increases by 8% in one year. If the initial population was $P_0$, what is the final population, $P_f$, at the end of the year?
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Coccal bacteria, with a mass of approximately $9.5 × 10^{-13}$ g each and a radius of approximately $0.5 \mu m$ each, form Diplococcal bacteria. Estimate the gravitational force between these two adjacent bacteria.
Coccal bacteria, with a mass of approximately $9.5 × 10^{-13}$ g each and a radius of approximately $0.5 \mu m$ each, form Diplococcal bacteria. Estimate the gravitational force between these two adjacent bacteria.
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Flashcards
Vector Addition
Vector Addition
The process of combining two or more vectors to determine their resultant vector.
Components of a Vector
Components of a Vector
The projections of a vector along the axes, typically x and y.
Trigonometric Functions
Trigonometric Functions
Functions like sine, cosine, and tangent used to relate angles and sides in right triangles.
Finding x-component
Finding x-component
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Finding y-component
Finding y-component
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Algebraic Sign of Components
Algebraic Sign of Components
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Right Triangle in Vector Problems
Right Triangle in Vector Problems
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Magnitude and Direction of a Vector
Magnitude and Direction of a Vector
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Resultant Vector
Resultant Vector
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Vector Component
Vector Component
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Magnitude of a Vector
Magnitude of a Vector
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Direction of a Vector
Direction of a Vector
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Free-Body Diagram
Free-Body Diagram
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Equations of Equilibrium
Equations of Equilibrium
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Resolving Forces
Resolving Forces
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Force in a Direction
Force in a Direction
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Fundamental Forces
Fundamental Forces
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Contact Forces
Contact Forces
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Net Force
Net Force
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Newton's First Law
Newton's First Law
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Free-Body Diagram (FBD)
Free-Body Diagram (FBD)
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Vector Quantities
Vector Quantities
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Inertia
Inertia
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SI Unit of Force
SI Unit of Force
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Scalar Quantity
Scalar Quantity
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Vector Quantity
Vector Quantity
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Vector Notation
Vector Notation
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Graphical Vector Addition
Graphical Vector Addition
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Resolving Vectors
Resolving Vectors
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Negative of a Vector
Negative of a Vector
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Gravitational Force Formula
Gravitational Force Formula
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Weight Formula
Weight Formula
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Gravitational Field Strength
Gravitational Field Strength
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Inverse Square Law
Inverse Square Law
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Normal Force
Normal Force
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Static Friction
Static Friction
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Force of Friction
Force of Friction
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Coccal Bacteria Mass
Coccal Bacteria Mass
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Force of Gravity
Force of Gravity
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Factor in Physics
Factor in Physics
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Percentage Increase
Percentage Increase
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Percentage Decrease
Percentage Decrease
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Weight Change in Airplane
Weight Change in Airplane
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Coccal Bacteria
Coccal Bacteria
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Newton's Law of Gravitation
Newton's Law of Gravitation
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Force Calculation Example
Force Calculation Example
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Study Notes
Unit 1, Chapter 2: Introductions to Vectors and Forces
- This chapter introduces vectors and forces.
- Scalars have magnitude and units, but no direction. Vector quantities have magnitude and direction.
- Scalars are added/subtracted like regular numbers.
- Adding vectors takes directions into account.
- A vector is indicated by an arrow over a boldface symbol (e.g., $\vec{F}$).
- The magnitude of a vector is represented by the symbol in italics (e.g., F). Magnitude can be positive or zero. It does not have a direction.
- Vectors are represented by arrows.
- The length of the vector arrow is proportional to its magnitude.
- The negative of a vector points in the opposite direction.
- The diagrams show graphical vector addition.
- Vectors can be added graphically using the tail-to-head method.
- Vectors can be added along the same straight line and the same direction.
- Adding vectors that start at the same point involves drawing a diagram (see images).
- Vectors can be added using components.
- Any vector can be expressed as a sum of vectors parallel to the x, y, and optionally, z axes.
- X, Y and Z components represent magnitude and direction along those axes.
- Components have magnitude, units, and an algebraic sign. The sign of the component indicates the direction along the axis.
- Finding components is called resolving the vector.
- The trigonometric functions can be used to find vector components. The Pythagorean theorem can be used to find the magnitude of a vector from its components.
- Problems can be solved using trigonometric functions, Pythagorean Theorem, and diagrams.
Scalars and Vectors
- A scalar quantity describes a physical quantity with only magnitude.
- A vector quantity describes a physical quantity with both magnitude and direction.
- Examples of scalars include mass, speed, distance, time, temperature, and energy.
- Examples of vectors include force, velocity, displacement, and acceleration.
Vector Representation
- Vectors are represented by arrows.
- The length of the arrow represents the magnitude of the vector.
- The direction of the arrow represents the direction of the vector.
Graphical Vector Addition
- Vectors can be added graphically using the tail-to-head method.
- Draw the first vector. Place the tail of the next vector at the head of the first vector.
- The resultant vector starts at the tail of the first vector and ends at the head of the last vector.
- Graphical methods are useful for visualizing vector addition, particularly in two dimensions.
Vector Addition Using Components
- Vectors can be added component-wise.
- Add the x-components of the vectors together.
- Add the y-components of the vectors together.
- Use the results to find the magnitude and direction of the resultant vector.
- In many cases, adding vectors using components is a more efficient method in determining the sum
Problem-Solving Strategy: Finding Components of a Vector
- Draw a right triangle.
- Determine a relevant angle.
- Use trigonometry functions to find magnitude of the components.
- Determine the algebraic sign for the component from the diagram.
Problem-Solving Strategy: Finding the Magnitude and Direction of a Vector
- Sketch the vector; identify its components.
- Draw a right triangle with the vector as the hypotenuse and its components as sides.
- Determine the appropriate angle.
- Use trigonometric functions to calculate the angle.
- Use the Pythagorean theorem to determine the magnitude of the vector.
Problem-Solving Strategy: Adding Vectors using Components
- Find the x and y components of each vector to be added.
- Add the x components with their algebraic signs.
- Add the y components with their algebraic signs.
- If necessary, use x and y components of the sum to find magnitude and direction of the sum.
Net Force
- The net force is the vector sum of all forces acting on an object.
- Object motion is determined by the net force.
Inertia and Equilibrium: Newton’s First Law of Motion
- For an object in equilibrium, the net force = 0.
- This means the sum of the forces in each direction (x, y, and z) is zero. (This implies zero acceleration.)
- An object in equilibrium has a constant velocity (i.e., a zero acceleration).
Forces
- Forces are vector quantities that have both magnitude and direction.
- Examples of forces include gravitational force, electromagnetic force, strong force, weak force, normal force, forces of friction (kinetic and static), and tension.
Free-Body Diagrams (FBD)
- An FBD is a simplified diagram showing all forces acting on a single object.
- Draw the object as a point (or a simple shape).
- Include all forces acting on the object in the diagram.
- Label all force vectors.
- Include relevant coordinate systems and angle measurements.
- Label forces exerted on another object are not included.
Definitions
- Normal Force (N): The force exerted by a surface on an object. This force is always perpendicular to the surface
- Force of Friction (f): The force exerted by a surface on an object that opposes the object's motion.
- Static Friction (fs): The force required to start the object's motion. It has a maximum value
- Kinetic Friction (fk): The force required to maintain the object's motion.
- Weight (W): The force of gravity on an object.
- Tension (T): The force exerted by a string, cord, or rope when it is pulled at its ends.
Universal Gravitation
- Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers (G=6.674 × 10⁻¹¹ N⋅m²/kg²).
Important Notes from Self Study Chapter One
- The word "factor" is often used in physics. It describes the ratio of new quantity to the old.
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Description
Questions cover gravitational force, free fall acceleration, weight calculation, normal force determination, and friction. Explore the concepts of static and kinetic friction. Analyze forces on slopes.