Chapter 9: Statics and Torque Flashcards
What is statics the study of?
The study of forces in equilibrium
What is the first necessary condition to achieve equilibrium?
The net external force on the system must be 0
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
True/False: If net F is 0 then the external force in ANY direction is 0
True
There are 2 types of equilibrium. What are they?
- Static equilibrium (motionless)
- Dynamic equilibrium (constant velocity)
What is the second condition necessary to achieve equilibrium?
Maintaining a constant angular velocity
Define torque
THe rotation equivalent of a force where magnitude, direction, and point of application are all incorporated in a physical quantity
What is the equation for torque?
ῖ = rFsinꝋ
What is the SI unit for torque?
Newtons * meters (N ∙ m)
Torque is calculated with reference to a….
pivot point
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
What are the 3 types of equilibrium?
Stable, neutral, unstable
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
Define restoring force
A force that moves back toward the equilibrium position
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
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 whichFlies
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
- Draw FBD. Large! Indicate forces and lever arms (lever arms are picked AFTER rotation axis)
- Pick x and y axes. Also pick rotation axis.
- Separate equations
I) Y equation: ∑Fy = 0
II) X equation: ∑Fx = 0
III) Rotation: ∑τ = 0 - Algebra to find the unknown
- 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:
- Assess what you know
i) d/r= 0.266 m
ii) rock mass = 445kg
iii) gravity = 9.81m/s
iv) L = ? - Find the needed equations
i) F = mg
ii) t = Fl (both man and rock)
iii) t1 = t2 - 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) - 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
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.
9.95%
Explanation:
- Assess what you have
i) Lrod = 1.75m
ii) Center point = 0.0415
iii) m1 = 1N
iv) m2 = 1N
v) x = Percentage of water - 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) - 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 - Plug in numbers and solve
i) x = [-m2g(L2/2) / m1g] / L1/2
ii) x = {[(-1N9.81)*(1.79 / 2)] / 1N} / 1.71m/2
iii) x = -8.77995 / 0.855
iv) x = -9.95
v) x = 9.95
