Forces, Circular Motion, and Gravitation

Question 1

Newton’s First Law

Answer 1

• An object will remain at rest, and an object in motion will continue to move with uniform velocity in a straight line, unless acted upon by an external force

Question 2

Newton’s Second Law

Answer 2

• A force acting on an object will give that object an acceleration in the direction of the foce. The acceleration of the object is directly proportional to the resultant force applied to the object and inversely proportional to the mass of the object
• F = ma
  
  • Units of force is a newton (N); kg-m/s²

Question 3

Newton’s Third Law

Answer 3

• If one object exerts a force on a second object, the second object will exert a reaction force on the first object which is equal in magnitude, but opposite in direction

Question 4

Newton’s Law of Gravitation

Answer 4

• The size of the force is proportional to the two masses, and it is inversely proportional to the square of the distance between them
• F = (GM₁M₂)/(r²)
  
  • ​G = 6.67 x 10^-11 N-m²/kg²

Question 5

What is Your Weight in an Elevator?

Answer 5

• Three forces
  
  • Weight of human (W = mg)
  • Force pushing up on human from scale (S)
  • Total force (ma)
• Force up minus force down equals total force
  
  • S - W = ma, S = W(1 + a/g)

Question 6

Arc Length

Answer 6

• S = θr
  
  • θ_radians = θ_degrees(π/180^o)
  • 2π_radians = 360^o

Question 7

Angular Velocity

Angular Acceleration

Answer 7

• ω = Δθ/Δt =v/r; ω = 2π/T
  
  • How fast theta is changing around a circular track
  • (Δθ)(1/Δt) = (ΔS/r)(1/Δt) = Δθ/Δt = v/r
  • ΔS/Δt = v
  • Is constant everywhere on a spinning object
• α = Δω/Δt = a/r
  
  • How fast is omega chaning around a circular track

Question 8

Where Does Velocity Point to On a Circle?

Answer 8

• Velocity is tangent to the circle

Question 9

Centripetal Acceleration

Answer 9

• Points to the middle of the cirlce
  
  • Is perpendicular to the velocity, which is tangental to the circular path
• a_c = vω = v(v/r) = v²/r
  
  • = (ωr)ω = ω²r

Question 10

Centripetal Force

Answer 10

• F_centripetal = m(v²/r)
  *

Question 11

f_{static max}

f_kinetic

Answer 11

• f_{static max} = μ_SN
• f_kinetic = * μ*_KN

Question 12

Mechanical Advantage

Answer 12

• Machine with a greater _mechanical advantage _ will require less applied force than a machine with less
• Mechanical advantage = (weight of object)/(applied force needed to support the object)

Question 13

Inclined Plane

Answer 13

• F_x = mgsinθ
• F_y = mgcosθ

Question 14

Pulleys

Answer 14

• Used to change the direction of a given force
• Multiple pulleys can be used to increase the system’s mechanical advantage
• Count number of vertical ropes supporting the lower pulley; divide the weight of the object by that number to get the weight for tension