Newton's Laws

Question 1

The First Law

Answer 1

Newton’s first law says that an object will continue in its state of motion unless compelled to change by a force impressed upon it

• An object at rest will stay at rest, an object in motion will stay in motion (at a constant speed in a straight line)
• No force= Δv
• Inertia: Property of objects, their natural resistance to changes in the state of motion
  
  • First Law also called law of inertia
  • Mass is a measure of inertia; the more mass an object has the more the object resists changing its velocity

Question 2

The Second Law

Answer 2

Acceleration, a, is directly proportional to the magnitude of the total, net force, (F_net) and inversely proportional to the object’s mass

• F_net= ma
• This law defines force

Question 3

Force

Answer 3

• The larger the force the larger the acceleration
• Forces are represented by vectors; they have magnitude and direction
  
  • If several different forces act on an object simultaneously, then the net force is the vector sum of all these forces (resultant force= net force)
    
    • There can be forces acting on an object without causing a net acceleration; this happens when the forces cancel each other out F_net= 0
• An object does not have to move in the direction of the net force in the samne way an object doesn’t have to move in the direction of acceleration
  
  • The relationshipo between the direction of net force and velocity is the same as the relationship between acceleration and velocity
    
    • Foward forces speed up objects, backward forces slow down objects, and forces perpendicular to the velocity are responsible for turning

Question 4

Newton

Answer 4

A force of 1 kg•m/s² is renamed 1 newton (N)

A medium sized apple weighs about 1 N

Question 5

Mass

Answer 5

The mass of an object is directly related to its weight

• The heavier an object is, the more mass it has
• Mass is measured in kilograms (kg)
• Mass measures an object’s inertia- resistance to acceleration
• Mass and weight are not the same thing

Question 6

The Third Law

Answer 6

If object 1 exerts a force on object 2, then object 2 exerts a force back on object 1, equal in strength but in the opposite direction

Question 7

Newton’s Law of Gravitation

Answer 7

Any two objects in the universe exert an attractive force on each other- the gravitational force- whose strength is proportional to the product of the objects’ masses and inversely proportional to the square of the distance between them

• G is the universal gravitational constant, 6.67 x 10^-11 N•m²/kg²
• F= G(m₁m₂)/r²
• Forces form along the line that joins the bodies and forms an action/reaction pair

Question 8

The Gravitational Attraction Due to An Extended Body

Answer 8

Newton’s law of gravitation is a statement about the force between two point particles

• Newton proved that a uniform sphere attracts another body as if all of the sphere’s mass were concentrated at its center
  
  • Newton’s law of gravitation can be applied to objects that are not small, relative to the distance between them
• r is the distance between the centers of mass of the two objects; for objects with uniform density this is the distance from center to center
• The force of gravity is very small unless at least one of the objects is large such as a planet or moon

Question 9

Point Particles

Answer 9

Objects that are very small in comparison with the distance between them

Question 10

Centripetal and velocity of satellite

Answer 10

Centripetal Force: mv²/R

Velocity of Satellite: v= squareroot(GM/R)

The Satellite’s speed doesn’t depend on its mass; even if it were a baseball, if its orbit radius were R then its orbit speed would still be given by the formula above

Question 11

Weight

Answer 11

Gravitational force exerted on it by earth (or whichever planet it is on)

• Since weight is a force, it can be computed by F_net= ma, a=g
  
  • F_w= mg
  • Mass and weight are proportional but not identical

Question 12

Mass Vs Weight

Answer 12

• The weight of an object is the gravitational force exerted on it by earth (or planet is on)
• Mass is an intristic property of an object that measures interia
• An object’s mass does not change with location
  
  • An object’s weight on the moon will be less than on earth but its mass would stay the same
• Mass and weight are proportional but not identical F_w= mg
• Mass is measured in kilograms, while weight is mesaured in newtons

Question 13

G vs g

Answer 13

• G is a universal constant equal to 6.67 x 10^-11 N•m²/kg²
• g depends on what planet or moon an object is on
• Near the surface:
  
  • mg= GMm/R²
    
    • M and R are the mass and radius of the planet or moon
    • g= GM/R² (cancelling m)

Question 14

Normal

Answer 14

Perpendicular

Question 15

Contact Force

Answer 15

When an object is in contact with a surface, the surface exerts a contact force on the object

Question 16

The Normal Force

Answer 16

The component of the contact force that’s perpendicular to the surface is called the normal force of the object

• Normal force prevents objects from falling through table tops or from falling through the floor
• Denoted by F_N or N( not to be confused with N for newton)
• Normal is not always equal to mg

Question 17

Friction

Answer 17

The component of the contact force that’s parallel to the surface is called the friction force on the object

• Friction, like normal force, arises from electrical interactions between atoms of the object and surface
• Two main categories:
  
  • Static friction
  • Kinetic (Sliding) friction
• Strength of friction force dependent on
  
  • Nature of the surfaces
    
    • Represented by the coefficient of friction, μ; the greater this number the stronger the friction force will be
  • Strength of the normal force

Question 18

Static Friction

Answer 18

Occurs when there is no relative motion between the object and the surface (no sliding)

F_{static friction, max}= μ_sF_N

• Equation for the magnitude of static friction force is for the maximum value
  
  • Static friction can vary, counteracting weaker forces that are less than the mimium force required to move an object
  • Static friction can take on all values, up to a certain maximum, and the maxmium static friction force must be overcome for the object to slide
    
    • Example, If maximum static force exerted is 50N and object is pushed with 20N, then the static friction force will be 20N in the opposite direction not 50N; the object won’t move: the net force on a stationary object must be zero
• The direction of F_{static friction}= F_f(static) is opposite to that of the intended motion

Question 19

Kinetic Friction

Answer 19

Occurs when there is relative motion (when there’s sliding)

F_{kinetic friction}= μ_kF_N

The direction of F_{kinetic friction}= F_f(kinetic) is opposite to that of motion (sliding)

Question 20

Static Friction Vs. Kinetic Friction

Answer 20

• Kinetic friction is generally weaker than static friction (it’s easier to keep an object sliding once it’s sliding than it is to start the object sliding in the first place)
• Two coffecients of friction
  
  • μ_s static friction
  • μ_k kinetic friction
• For a given pair of surfaces μ_k < μ_s is virtually always true

Question 21

Person walking static or kinetic friction

Answer 21

For a person walking, the friction between the person’s shoes and the floor is static (no sliding) and is directed foward (in the direction the person is walking) The person pushes on the floor in the backward direction, static friction prevents it from moving backward and so therefore must me forward

Objects that are rolling without slipping, rolling normally, not skidding, roll because of static friction

Question 22

Pulleys

Answer 22

Devices that change the direction of the tension force in the cords that slide over them

• In the case of two single masses m₁ and m₂ that are attatched to a pulley and cord, the downward forces are due to the weight (mass and gravity exerted on it) of the masses
  
  • The upward forces are due to the tension (T) in the cord

Question 23

Inclined Plane

Answer 23

Ramp

• If object of mass, m, is on the ramp, then the force of gravity on the object, F_w= mg has two components
  
  • One that is parallel to the ramp (mgsinθ)
  • One that is normal to the ramp (mgcosθ)
  • θ is the incline angle
• The force driving the block down the inclined plane is the component of the block’s weight that’s parallel to the ramp: mgsinθ

Question 24

Incline plane Mneomic

Answer 24

mgsinθ is the component of gravity down the inclined plane by thinking (sine) equals (sliding)

Question 25

Short hand Pulley

m= 2kg

M= 10kg

coefficient of kinetic friction between the small block and tabletop is 0.5

what is the acceleration of the blocks

Answer 25

Mg- M_kmg= (M + m)a

Mg= forward force

M_kmg= backward force

(M + m)= total mass