4. Mechanics Part 3

Question 1

What is the formula for work done by a constant force?

Answer 1

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

Question 2

t or f, opposite to torque, work is only concerned with the parallel component of force.

Answer 2

True,
cos(0) = 1, gives maximum work

This is opposite torque in which maximum torque is achieved when force is perpendicular (to x).

Question 3

How do you find total work of a system (e.g. a block sliding down a platform)?

Answer 3

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

Question 4

t or f, work is a scalar.

Answer 4

true, work has no direction.

Question 5

When is work negative?

Answer 5

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.

Question 6

On a position (x) vs force (y), what is the area under the curve?

Answer 6

The area under the curve is work!

Question 7

What is power, what is its formula? What is its units?

Answer 7

Power measures how fast work gets done.

P = W / t

the units are joules / second = Watts

Question 8

How can we find power if we know velocity? Assume that the force is parallel with the direction.

Answer 8

P = W / t = Fd / t

d / t = v therefore, P = Fv

Note that we need cosθ if F and d are not parallel.

Question 9

What is a calorie? What is a Calorie? How do they relate to joules?

Answer 9

calorie = 4.2 joules

Calorie = kilo-calorie = 4200 joules

Question 10

t or f, energy is the ability to do work (the ability to apply a force over a distance)

Answer 10

true

Question 11

What is kinetic energy? What is the formula?

Answer 11

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

Question 12

Why is the work done in circular motion zero?

Answer 12

W = Fdcosθ

Force points inwards, velocity (i.e. position) points tangent to the circle. Cos(90) = 0.

Question 13

What is the Work-Energy theorem?

Answer 13

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

Question 14

t or f, if an objects speed is constant, then no work is being done.

Answer 14

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.

Question 15

What is potential energy? What is gravitational PE?

Answer 15

Potential energy is the energy an object has due to its position (gravity, electricity, and elastic)

ΔPEg = -W (done by gravity)

Question 16

If the change in gravitational PE equals the negative work done by gravity, what formula can we use to find ΔPE?

Answer 16

ΔPEg = -W

to lift an object, we must apply -Fg.
F = -Fg = -mg

W = F x d

W = -mgd = ΔPEg

Question 17

t or f, if we are lifting an object, work done by gravity is working against you (negative), therefore, ΔPE is positive.

Answer 17

true (+mgh)

if something falls, ΔPE is negative (-mgh)

Question 18

Why is gravity a conservative force?

Answer 18

Because it acts as a state function, independent of the path taken.
Note that PE can only be defined for conservative forces.

Question 19

What is total mechanical energy?

Answer 19

E = KE + PE

Question 20

What is an objects total mechanical energy at its apex when shot straight up into the air?

Answer 20

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

Question 21

What is conservation of total mechanical energy?

Answer 21

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

Question 22

Conservation of total mechanical energy: what if we include friction?

Answer 22

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)

Question 23

What is a simple machine?

Answer 23

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.

Question 24

A simple machine is said to give you a mechanical advantage. What is this? How is it calculated?

Answer 24

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)

Question 25

What is efficiency? How is it calculated?

Answer 25

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%

Question 26

What is the formula for momentum?

Answer 26

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

Question 27

What is the Impulse-momentum theorem?

Answer 27

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.

Question 28

What is the mnemonic to remember the impulse-momentum theorem?

Answer 28

I AM FAT

J = Δp = mΔv = FΔt

I = Δm = FΔt

Question 29

What is the law of conservation of momentum?

Answer 29

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.

Question 30

Explain elastic, inelastic, and perfectly inelastic collisions.

Answer 30

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.

Question 31

t or f, when dealing with momentum, the sign of velocities matters.

Answer 31

Yes, always (momentum is a vector)

Question 32

t or f, when dealing with collision questions, always use conservation of momentum.

Answer 32

True, although elastic collisions (no energy loss) can use the conservation of energy, using momentum is safer.