Chapter 9: Statics and Torque Flashcards by Miranda Miller

What is statics the study of?

The study of forces in equilibrium

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What is the first necessary condition to achieve equilibrium?

The net external force on the system must be 0

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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)

net F = 0

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

True

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There are 2 types of equilibrium. What are they?

Static equilibrium (motionless)
Dynamic equilibrium (constant velocity)

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What is the second condition necessary to achieve equilibrium?

Maintaining a constant angular velocity

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Define torque

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

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What is the equation for torque?

ῖ = rFsinꝋ

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What is the SI unit for torque?

Newtons * meters (N ∙ m)

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Torque is calculated with reference to a….

pivot point

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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

Equilibrium, stable

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

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What are the 3 types of equilibrium?

Stable, neutral, unstable

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Define stable equilibrium

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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Define restoring force

A force that moves back toward the equilibrium position

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Define unstable equilibrium

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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Define neutral equilibrium

When the equilibrium is independent of displacements from its original position

Ex: Marble on a flat surface

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

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

What are the 4 steps to solving static equilibrium situations?

Determine whether the system is static
Draw a FBD
Solve by applying either or both of the conditions for equilibrium
Double check

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

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

basically no rotation = static

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

net F = 0, net ῖ = 0

Define mechanical advantage (MA)

The ratio output to input force

T/F: Input force must equal output force

True

What is mechanical advantage in equation form?

MA = Fo/Fi

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

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

liFi = loFo

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

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

MA = Fo / Fi = li / lo

define center of gravity

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

Define dynamic equilibrium

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

Define perpendicular lever arm

the shortest distance from the pivot point to the line along which F lies

Define static equilibrium

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

What is net torque in equation form?

∑T = T1 + T2

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

t = Fl

How is lift calculated?

ℓ = 1/2 L cos a ℓ = lift L = length a = alpha (angular acceleration)

Define equilibrium

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

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

Tan = sin / cos

5 steps for solving statics

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

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?

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

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?

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

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