Key Equations
ΣF=ma (Net external force = mass x acceleration) (= vector sum)
ΣF=ma (Net external force = mass x acceleration) (= vector sum)
Key Terms
Forces: a push or a pull exerted on an object
Weight: force of an object due to gravitational pull (mass x 10 (gravity) = weight)
Mass: quantity of matter measured in kilograms
Field forces: do not involve physical contact between two objects
Contact Forces: result from physical contact between to objects
Force Diagrams: diagrams that show force vectors as arrows
Free-Body Diagram: used to analyze only the forces affecting the motion of a single object
Inertia: an object in motion stays in motion and maintains a constant velocity unless acted upon by a force
External force: a single force that acts on an object as a result of the interaction between the object and its environment
Net external force: the vector sum of all the forces acting on the object
Equilibrium: an object at rest or moving with a constant velocity are said to be in equilibrium
Static Friction: the resistive force that keeps an object from moving (Fs)
Kinetic Friction: the frictional force acting on an object in motion
Coefficient of Friction: the quantity that expresses the dependence of frictional forces on the particular surfaces in contact
Section 1: Newton's First Law
Newton’s first law is often referred to as the law of inertia because it states that in the absence of forces, a body will preserve its state of motion
Newton's Second Law: the acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the object’s mass
The Normal Force
-When the force of static friction is as great as it can be without the object moving, it reaches its maximum value
Section 4: Universal Gravitation
Practice
Multiple Choice Questions:
1.) An astronaut applies a force of 500 N to a satellite located in space and causes it to accelerate at 7.0 m/s2. What is the mass of the satellite?
A. 50kg
B. 71kg
C. 135kg
D. 441kg
E. 3,500kg
2.) The unit for coefficient of friction in the SI system is ___.
A. m/s2
B. kg
C. slug
D. N
E. It does not have a unit
3.) What is the approximate mass of a 7.5 kg book on the moon where the gravitational acceleration is 1.67 m/s2?
A. 12.5kg
B. 7.5 kg
C. 75kg
D. 7.5N
E. 12.5N
4.) A 15kg mass is sliding along a frictionless floor with an acceleration of 5 m/s2. What is the magnitude of the net force acting on the mass?
A. 15N
B. 20N
C. 3N
D. 75N
E. 10N
5.) A constant force acts on a mass. If the mass were tripled but the force remained constant, the acceleration of the mass would be ____.
A. nine times as much
B. three times as much
C. unchanged
D. one-third as much
E. one-ninth as much
6.) A stone of mass 1 kg and weight 10N falls through the air. The air resistance acting on the stone is 2N. What is the acceleration of the stone?
A. 12m/s2
B. 9.8m/s2
C. 8 m/s2
D. 5 m/s2
E. 2m/s2
7.) In which of the following examples is a net force of zero acting on the object in question?
I- A car drives around a circular racetrack at a constant speed
II- A person pushes on a door to hold it shut
III- A ball, rolling across a grassy field, slowly comes to a stop
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
8.) If an object is at rest or moving with a constant velocity, then ____.
A. there are no forces acting on the object
B. the net force acting on the object is zero
C. the object is accelerating
D. the object is losing mass
E. None of the above is true
9.) Two vectors A and B, have components Ax = -2, Ay = 3, Bx= 1, and By = 4. The magnitude of A-B is most nearly?
A. 3
B. 6
C. 8
D. 5
E. 7
10.) A ball falls freely toward the earth. If the action force is the earth pulling down on the ball, the reaction force is ___.
A. the ball pulling up on the earth
B. air resistance acting on the ball
C. the ball striking the earth when it lands
D. the inertia of the ball
E. there is no reaction force in this case
ANSWER KEY: 1.) B 2.) E 3.) B 4.) D 5.) D 6.) C 7.) B 8.) B 9.) A 10.) A
Open Ended Questions
1.) A 10kg crate is pushed with a horizontal force FA on a flat surface. The coefficients of friction are us = 0.22 and uk= 0.19. Assuming the crate starts at rest, fill in the table below with the appropriate friction force and acceleration.
2.) A 50kg box is at rest on a table. A kid pulls on the box with a force of 400N at an angle of 30˚ above the horizontal. The coefficients of static and kinetic fricitons are respectively 0.2 and 0.3.
A.) Determine whether the box is going to move or not
B.) Calculate the acceleration of the box
C.) With the kid pulling at an angle of 30˚, what would be the minimum amount of force required to get the box moving and what would have been the resulting acceleration?
3.) A book is located on a wooden board and starts sliding when the board is inclined at 42˚. Once it starts sliding, it takes 2s for the book to reach down the bottom of the 1.2m long wooden board. Use this information to calculate the coefficient of kinetic friction and the coefficient of static friction between the book and the wooden board.
Video Links
https://www.youtube.com/watch?v=yhG_ArxmwRM
This video describes gravitation in detail, which will allow one to easily understand universal gravitation. It covers both the equation and the principles behind it.
https://www.youtube.com/watch?v=NYVMlmL0BPQ
This video describes Newton's laws, which govern the principles of forces and motion. It covers all three laws in detail, and goes over what a free body diagram is. It includes an explanation of why objects move, and how specifically forces affect motion.
Forces: a push or a pull exerted on an object
Weight: force of an object due to gravitational pull (mass x 10 (gravity) = weight)
Mass: quantity of matter measured in kilograms
Field forces: do not involve physical contact between two objects
Contact Forces: result from physical contact between to objects
Force Diagrams: diagrams that show force vectors as arrows
Free-Body Diagram: used to analyze only the forces affecting the motion of a single object
Inertia: an object in motion stays in motion and maintains a constant velocity unless acted upon by a force
External force: a single force that acts on an object as a result of the interaction between the object and its environment
Net external force: the vector sum of all the forces acting on the object
Equilibrium: an object at rest or moving with a constant velocity are said to be in equilibrium
Static Friction: the resistive force that keeps an object from moving (Fs)
Kinetic Friction: the frictional force acting on an object in motion
Coefficient of Friction: the quantity that expresses the dependence of frictional forces on the particular surfaces in contact
Section 1: Newton's First Law
Newton’s first law is often referred to as the law of inertia because it states that in the absence of forces, a body will preserve its state of motion
- The inertia of an object is proportional to its mass (the greater the mass, the greater the inertia, and therefore the less the object accelerates under an applied force)
- Acceleration is determined by net external force
- Note that there is a difference between external force and net external force
- External force: a single force that acts on an object as a result of the interaction between the object and its environment
- Net external force: the vector sum of all the forces acting on the object
- An object traveling at a constant velocity will have a net external force of zero
- Net external force can be found by finding the sum of the resultant vectors of each of the external forces
Newton's Second Law: the acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the object’s mass
- Force is proportional to mass and acceleration
- If equal forces are applied to objects with different masses, the object with the greater mass will have a smaller acceleration and vice versa
- Simplified definition: every action has an equal and opposite reaction
- Forces always exist in pairs
- Action-reaction pair: the forces mutually exerted between two forces when when they interact with each other
- Field forces also exist in pairs (force of gravity (earth) on chair and force of chair on earth)
The Normal Force
- A force that is equal in magnitude to Fg for an object, but in a different direction as Fg
- A stationary object is in equilibrium due to Fg and the normal force (Fn) being equal
- Normal force is perpendicular to the surface the object rests on
- Friction opposes the applied force
- Static Friction: the resistive force that keeps an object from moving (Fs)
-When the force of static friction is as great as it can be without the object moving, it reaches its maximum value
- Kinetic Friction: the frictional force acting on an object in motion
- The net external force of an object is equal to difference between the applied force and the force of kinetic friction
- Frictional forces arise from complex interactions of contacting surfaces at the microscopic level
- When two surfaces are stationary they stick together at contact points (adhesion), which is caused by electrostatic forces between molecules of the two surfaces
- Because of adhesion, it takes greater force to cause an object to begin moving rsther than to keep it moving.
- The force of friction is proportional to the normal force
- Friction depends on the surfaces in contact and the composition and qualities of the surfaces in contact
- Coefficient of Friction: the quantity that expresses the dependence of frictional forces on the particular surfaces in contact
- The coefficient of friction is a ratio between the force of friction and the normal force between two surfaces
Section 4: Universal Gravitation
- Newton's law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Practice
Multiple Choice Questions:
1.) An astronaut applies a force of 500 N to a satellite located in space and causes it to accelerate at 7.0 m/s2. What is the mass of the satellite?
A. 50kg
B. 71kg
C. 135kg
D. 441kg
E. 3,500kg
2.) The unit for coefficient of friction in the SI system is ___.
A. m/s2
B. kg
C. slug
D. N
E. It does not have a unit
3.) What is the approximate mass of a 7.5 kg book on the moon where the gravitational acceleration is 1.67 m/s2?
A. 12.5kg
B. 7.5 kg
C. 75kg
D. 7.5N
E. 12.5N
4.) A 15kg mass is sliding along a frictionless floor with an acceleration of 5 m/s2. What is the magnitude of the net force acting on the mass?
A. 15N
B. 20N
C. 3N
D. 75N
E. 10N
5.) A constant force acts on a mass. If the mass were tripled but the force remained constant, the acceleration of the mass would be ____.
A. nine times as much
B. three times as much
C. unchanged
D. one-third as much
E. one-ninth as much
6.) A stone of mass 1 kg and weight 10N falls through the air. The air resistance acting on the stone is 2N. What is the acceleration of the stone?
A. 12m/s2
B. 9.8m/s2
C. 8 m/s2
D. 5 m/s2
E. 2m/s2
7.) In which of the following examples is a net force of zero acting on the object in question?
I- A car drives around a circular racetrack at a constant speed
II- A person pushes on a door to hold it shut
III- A ball, rolling across a grassy field, slowly comes to a stop
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
8.) If an object is at rest or moving with a constant velocity, then ____.
A. there are no forces acting on the object
B. the net force acting on the object is zero
C. the object is accelerating
D. the object is losing mass
E. None of the above is true
9.) Two vectors A and B, have components Ax = -2, Ay = 3, Bx= 1, and By = 4. The magnitude of A-B is most nearly?
A. 3
B. 6
C. 8
D. 5
E. 7
10.) A ball falls freely toward the earth. If the action force is the earth pulling down on the ball, the reaction force is ___.
A. the ball pulling up on the earth
B. air resistance acting on the ball
C. the ball striking the earth when it lands
D. the inertia of the ball
E. there is no reaction force in this case
ANSWER KEY: 1.) B 2.) E 3.) B 4.) D 5.) D 6.) C 7.) B 8.) B 9.) A 10.) A
Open Ended Questions
1.) A 10kg crate is pushed with a horizontal force FA on a flat surface. The coefficients of friction are us = 0.22 and uk= 0.19. Assuming the crate starts at rest, fill in the table below with the appropriate friction force and acceleration.
2.) A 50kg box is at rest on a table. A kid pulls on the box with a force of 400N at an angle of 30˚ above the horizontal. The coefficients of static and kinetic fricitons are respectively 0.2 and 0.3.
A.) Determine whether the box is going to move or not
B.) Calculate the acceleration of the box
C.) With the kid pulling at an angle of 30˚, what would be the minimum amount of force required to get the box moving and what would have been the resulting acceleration?
3.) A book is located on a wooden board and starts sliding when the board is inclined at 42˚. Once it starts sliding, it takes 2s for the book to reach down the bottom of the 1.2m long wooden board. Use this information to calculate the coefficient of kinetic friction and the coefficient of static friction between the book and the wooden board.
Video Links
https://www.youtube.com/watch?v=yhG_ArxmwRM
This video describes gravitation in detail, which will allow one to easily understand universal gravitation. It covers both the equation and the principles behind it.
https://www.youtube.com/watch?v=NYVMlmL0BPQ
This video describes Newton's laws, which govern the principles of forces and motion. It covers all three laws in detail, and goes over what a free body diagram is. It includes an explanation of why objects move, and how specifically forces affect motion.