4. Mechanics Part 3 Flashcards
What is the formula for work done by a constant force?
Work is the energy of of applying a force over a distance
W = Fdcosθ
θ is the angle between F and d
the units are Joules
t or f, opposite to torque, work is only concerned with the parallel component of force.
True,
cos(0) = 1, gives maximum work
This is opposite torque in which maximum torque is achieved when force is perpendicular (to x).
How do you find total work of a system (e.g. a block sliding down a platform)?
One must find the work done by each force (over a given distance) and then add to find total work.
OR
find Fnet first and then multiply it by distance
t or f, work is a scalar.
true, work has no direction.
When is work negative?
W = Fdcosθ (F and d are always positive)
work is negative when cosθ is negative. This occurs when θ is an obtuse angle (draw the quadrants).
Essentially, work is negative if the force applied is opposite the direction of movement.
On a position (x) vs force (y), what is the area under the curve?
The area under the curve is work!
What is power, what is its formula? What is its units?
Power measures how fast work gets done.
P = W / t
the units are joules / second = Watts
How can we find power if we know velocity? Assume that the force is parallel with the direction.
P = W / t = Fd / t
d / t = v therefore, P = Fv
Note that we need cosθ if F and d are not parallel.
What is a calorie? What is a Calorie? How do they relate to joules?
calorie = 4.2 joules
Calorie = kilo-calorie = 4200 joules
t or f, energy is the ability to do work (the ability to apply a force over a distance)
true
What is kinetic energy? What is the formula?
Kinetic energy is the energy an object has due to movement.
Fd = KE = 1/2mv^2
units = joules
This formula can be found using the last kinematics equation and f = ma
Why is the work done in circular motion zero?
W = Fdcosθ
Force points inwards, velocity (i.e. position) points tangent to the circle. Cos(90) = 0.
What is the Work-Energy theorem?
Work done on an object is equal to the change in kinetic energy of that object
Work = ΔKE
Therefore, we do not need to know force or displacement to find work done.
essentially mechanical energy (work) transfers to kinetic energy.
W = 1/2mvf^2 - 1/2mvi^2
t or f, if an objects speed is constant, then no work is being done.
True. The work-energy theorem indicates that W = ΔKE. Since mass cannot change, if an objects velocity does not change either, then ΔKE = 0 = work.
What is potential energy? What is gravitational PE?
Potential energy is the energy an object has due to its position (gravity, electricity, and elastic)
ΔPEg = -W (done by gravity)
If the change in gravitational PE equals the negative work done by gravity, what formula can we use to find ΔPE?
ΔPEg = -W
to lift an object, we must apply -Fg.
F = -Fg = -mg
W = F x d
W = -mgd = ΔPEg
t or f, if we are lifting an object, work done by gravity is working against you (negative), therefore, ΔPE is positive.
true (+mgh)
if something falls, ΔPE is negative (-mgh)
Why is gravity a conservative force?
Because it acts as a state function, independent of the path taken.
Note that PE can only be defined for conservative forces.
What is total mechanical energy?
E = KE + PE
What is an objects total mechanical energy at its apex when shot straight up into the air?
since at its apex, velocity = 0, KE = 0.
E = mgh
at the very bottom of the path, right before it hits the ground, h = 0, PE = 0, and E = 1/2mv^2
What is conservation of total mechanical energy?
If only conservative forces are acting on an object (i.e. no friction), then an objects total energy will remain the same throughout motion.
KEi + PEi = KEf + PEf
Conservation of total mechanical energy: what if we include friction?
When friction acts, total mechanical energy is not actually fully conserved.
KEi + PEi +Wf = KEf + PEf
Wf = work done by friction. (this will be negative work)
What is a simple machine?
A simple machine is a device that allows someone to use less force to accomplish the same task. Simple machines do the same amount of work as if no machine was used, but with less applied force.
A simple machine is said to give you a mechanical advantage. What is this? How is it calculated?
Mechanical advantage is the quantifiable measure of how much less force you need with a simple machine verses without.
MA = Force (no machine) / Force (machine)
What is efficiency? How is it calculated?
Efficiency explains how much of a devices work goes to the task at hand. In the real world, energy is lost to the surroundings (sound, heat, etc).
Eff = (W out / E in) x 100%
If we push with 100 N, but 10 N goes to heat, then
Eff = 90 / 100 = 90%
What is the formula for momentum?
p = mv
note that since velocity is a vector, momentum (p) is a vector pointing in the same direction as velocity.
momentum has no special units = kg m / s
What is the Impulse-momentum theorem?
F = ma F = m x Δv / Δt
FΔt = mΔv = Δp = J
J is impulse, which measures the change in momentum. Using Newtons second law, we also see that Impulse also equals the force delivered multiplied by the time its being delivered.
What is the mnemonic to remember the impulse-momentum theorem?
I AM FAT
J = Δp = mΔv = FΔt
I = Δm = FΔt
What is the law of conservation of momentum?
Total momentum of a system remains constant.
Δp system = 0
pf = pi
Note that if outside forces come into play, conservation may no longer hold up.
Explain elastic, inelastic, and perfectly inelastic collisions.
momentum is always conserved.
elastic = KE is also conserved
inelastic = KE is not conserved
perfectly inelastic = KE is not conserved and the two objects stick together after the collision.
t or f, when dealing with momentum, the sign of velocities matters.
Yes, always (momentum is a vector)
t or f, when dealing with collision questions, always use conservation of momentum.
True, although elastic collisions (no energy loss) can use the conservation of energy, using momentum is safer.
