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College Physics - PH 201 > Chapter 9: Statics and Torque > Flashcards

Chapter 9: Statics and Torque Flashcards

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1
Q

What is statics the study of?

A

The study of forces in equilibrium

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2
Q

What is the first necessary condition to achieve equilibrium?

A

The net external force on the system must be 0

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3
Q

What is the mathematical expression for the net external force on a system equalling zero? (the first necessary condition for a system to be at equilibrium)

A

net F = 0

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4
Q

True/False: If net F is 0 then the external force in ANY direction is 0

A

True

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5
Q

There are 2 types of equilibrium. What are they?

A
  1. Static equilibrium (motionless)
  2. Dynamic equilibrium (constant velocity)
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6
Q

What is the second condition necessary to achieve equilibrium?

A

Maintaining a constant angular velocity

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7
Q

Define torque

A

THe rotation equivalent of a force where magnitude, direction, and point of application are all incorporated in a physical quantity

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8
Q

What is the equation for torque?

A

ῖ = rFsinꝋ

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9
Q

What is the SI unit for torque?

A

Newtons * meters (N ∙ m)

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10
Q

Torque is calculated with reference to a….

A

pivot point

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11
Q

It is one thing to have a system in _____, it is another for it to be _____

A. balance, moving
B. Equilibrium, stable
C. movement, balanced
D. stableness, equal

A

Equilibrium, stable

It is one thing to have a system in equilibrium, it is another for it to be stable

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12
Q

What are the 3 types of equilibrium?

A

Stable, neutral, unstable

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13
Q

Define stable equilibrium

A

When displaced from equilibrium, it experiences a net force or torque in a direction opposite to the direction of the displacement.

Ex: Marble at the bottom of a bowl

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14
Q

Define restoring force

A

A force that moves back toward the equilibrium position

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15
Q

Define unstable equilibrium

A

When displaced, it experiences a net force or torque in the same direction as the displacement from equilibrium

Ex: Ball on top of a hill

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16
Q

Define neutral equilibrium

A

When the equilibrium is independent of displacements from its original position

Ex: Marble on a flat surface

17
Q

What is the “critical point” causes a system to fall out of equilibrium?

A

When the center of gravity is no longer above the base of support

18
Q

What are the 4 steps to solving static equilibrium situations?

A
  1. Determine whether the system is static
  2. Draw a FBD
  3. Solve by applying either or both of the conditions for equilibrium
  4. Double check
19
Q

How do you determine whether a system is in static equilibrium?

A

It is always a static equilibrium when the acceleration of the system is 0 and accelerated rotation does not occur

basically no rotation = static

20
Q

What are the two conditions necessary for equilibrium in equation form?

A

net F = 0, net ῖ = 0

21
Q

Define mechanical advantage (MA)

A

The ratio output to input force

22
Q

T/F: Input force must equal output force

A

True

22
Q

What is mechanical advantage in equation form?

A

MA = Fo/Fi

MA = mechanical advantage
Fo = force out
Fi = force input

23
Q

How is the equilibrium between input and output force expressed in mathematical form?

A

liFi = loFo

li = Initial length
Fi = initial force
Io = final length
Fo = final force

24
Q

What 2 ways can the liFi=loFo equation be rearranged?

A

MA = Fo / Fi = li / lo

25
Q

define center of gravity

A

The point where the total weight of the body is assumed to be concentrated

26
Q

Define dynamic equilibrium

A

a state of equilibrium in which the net external force and torque on a system moving with constant velocity are zero

27
Q

Define perpendicular lever arm

A

the shortest distance from the pivot point to the line along whichFlies

28
Q

Define static equilibrium

A

A state of equilibrium in which the net external force and torque acting on a system is zero

AND

equilibrium in which the acceleration of the system is zero and accelerated rotation does not occur

29
Q

What is net torque in equation form?

A

∑T = T1 + T2

30
Q

How to F (force), l (lever arm), and t (torque) relate to each other?

A

t = Fl

31
Q

How is lift calculated?

A

ℓ = 1/2 L cos a

ℓ = lift
L = length
a = alpha (angular acceleration)

32
Q

Define equilibrium

A

A system is in equilibrium if there is no net force on it, and no net torque on

Aka:
∑Fx = 0
∑Fy = 0
∑τ = 0

33
Q

How do cos, sin, and tan relate to each other?

A

Tan = sin / cos

34
Q

5 steps for solving statics

A
  1. Draw FBD. Large! Indicate forces and lever arms (lever arms are picked AFTER rotation axis)
  2. Pick x and y axes. Also pick rotation axis.
  3. Separate equations
    I) Y equation: ∑Fy = 0
    II) X equation: ∑Fx = 0
    III) Rotation: ∑τ = 0
  4. Algebra to find the unknown
  5. Interpret/express answer
35
Q

A homeowner is trying to move a stubborn rock from his yard. By using a metal rod as a level arm and a fulcrum (or pivot point), the homework will have a better chance of moving the rock. The homeowner places the fulcrum a distance of d = 0.266m from the rock, which has a mass of 445kg, and fits one end of the rod under the rock’s center of weight. Assume the acceleration due to gravity is 9.81m/s

If the homeowner can apply a maximum force of 615 N at the other end of the rod, what is the minimum total length (L) of the rod required to move the rock?

A

2.15 m

Explanation:

  1. Assess what you know
    i) d/r= 0.266 m
    ii) rock mass = 445kg
    iii) gravity = 9.81m/s
    iv) L = ?
  2. Find the needed equations
    i) F = mg
    ii) t = Fl (both man and rock)
    iii) t1 = t2
  3. Plug in numbers
    i) Force of rock: F = mg, F = 445kg * 9.81m/s, F = 4365.45N
    iia) Torque of rock: t = Fl, t= 4365.45N * 0.266m = 1161.2 Nm
    iib) Torque of man: t =Fl, t = 615N * (L - 0.266)
  4. Set equal to each other and solve
    i) 1161.2 Nm = 615N * (L - 0.266m)
    ia) Divide both sides by 615N
    ii) 1.88 NM = L - 0.266m
    iia) Add 0.266m to both sides
    iii) L = 2.15 m
36
Q

While on a camping trip, a man would like to carry water from the lake to his campsite. He fills two, non-identical buckets with water and attaches them to a 1.75m long rod. Since the buckets are not identical, he finds that the rod balances about a point located at a length l = 0.0415m to the left from its midpoint. Assume bucket 1 is on the left and bucket 2 is on the right. The weight of the rod and empty buckets is neglible compared to the weight of the water.

Which bucket holds more water?

A

Bucket 1

Explanation: Since the balance point is to the left of the mid point and bucket 1 is to the left of the midpoint it can be assumed bucket 1 contains more water

37
Q

While on a camping trip, a man would like to carry water from the lake to his campsite. He fills two, non-identical buckets with water and attaches them to a 1.75m long rod. Since the buckets are not identical, he finds that the rod balances about a point located at a length l = 0.0415m to the left from its midpoint. Assume bucket 1 is on the left and bucket 2 is on the right. The weight of the rod and empty buckets is neglible compared to the weight of the water.

Assuming the empty buckets weight 1N, and bucket 1 contains more water, calculate the percentage of how much more water it contains then bucket 2.

A

9.95%

Explanation:

  1. Assess what you have
    i) Lrod = 1.75m
    ii) Center point = 0.0415
    iii) m1 = 1N
    iv) m2 = 1N
    v) x = Percentage of water
  2. Find needed equations
    i) 0 = ∑τ
    ii) ∑τ = t1 + t2
    iii) t = Fl
    iiia) t = mg(L/2)
    2a. Knowing that Bucket 1 has more mass because of the water we can assume bucket 1 is (1N + x)
  3. Rearrange equations
    i) 0 = m1g * (L1/2x) + mg2 * (L2/2)
    ia) -mg2 * (L2/2) to both sides
    ii) -mg2 * (L1/2) = m1g * (L2/2x)
    iia) Divide both sides by m1g
    iii) -m2g(L2/2) / m1g = L1/2x
    iiia) divide L1/2
    iv) x = [-m2g    (L2/2) / m1g] / L1/2
  4. Plug in numbers and solve
    i) x = [-m2g(L2/2) / m1g] / L1/2
    ii) x = {[(-1N    9.81)*(1.79 / 2)] / 1N} / 1.71m/2
    iii) x = -8.77995 / 0.855
    iv) x = -9.95
    v) x = 9.95

College Physics - PH 201 (10 decks)

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