Mechanics 1-3: Forces, Torque, Work, Conservation

Question 1

What is force?

Answer 1

A force is a push or pull exerted by one object on another.

Question 2

What is Newton’s first law?

Answer 2

It’s known as the law of inertia - an object’s natural resistance to change in their state of motion. Objects don’t suddenly start moving on their own. An object already moving doesn’t change its velocity. Something must exert a net force. No net force = no acceleration.

Question 3

What is mass.

Answer 3

How much matter is contained in an object. It’s measured in kg.

Question 4

A space probe is heading towards Pluto at a constant speed of 57800 km/hr. What can you assume about this scenario given no other information?

Answer 4

You assume constant speed and direction(velocity). Remember from Newton’s first law, the spaceship is suspended in space because the net force on the probe up and down must be zero.

Question 5

What is Newton’s second law?

Answer 5

Fnet = ma; applied net forces causes change in motion. A net forces causes a change in acceleration and thus a change in velocity. Fnet is the sum of all the forces that act ON the object.

Question 6

True or false. Forces are vectors.

Answer 6

True. Forces have a magnitude and direction. You can add forces. Fnet and acceleration point in the same direction.

Question 7

True or false. If Fnet = 0, then acceleration is 0 and thus velocity is 0.

Answer 7

It’s a trap, ho! Fnet = 0 means an object won’t accelerate but it doesn’t mean it’s not moving. Think Newton’s 1st law. If an object is already moving at 100m/s north, it will continue to do so unless a net force acts on it.

Question 8

What is the units for force?

Answer 8

kgm/S^2

Question 9

What Newton’s 3rd law?

Answer 9

If object 1 exerts a force on object 2 (F12), then object 2 exerts a force (F21), on object 1. For every action, there is an equal and opposite reaction. F12 = (-)F21

Question 10

For Newton’s 3rd law, does it mean the effects on the objects on one another are the same? Shouldn’t forces just cancel each other out?

Answer 10

The effects on the forces are only the same if the objects are identical. Masses of the object might be different.

Question 11

What is the difference between weight and mass?

Answer 11

The weight of an object is the gravitational force exerted on it by a planet/moon. Mass is an intrinsic property - how much matter is contained in something.

Question 12

What is the formula for weight?

Answer 12

Weight is a force. w = mg.

Question 13

What is Newton’s Law of Gravitation?

Answer 13

Every object in the universe exerts a gravitation pull on every other object. Fgravity = (GMm)/r^2; G is a constant of proportionality = 6.7*10^-11 (Nm^2/kg^2). Note this is an action reaction pair! Dont memorize constant.

Question 14

What will happen to the gravitation force between two objects if the distance between them is doubled or halved?

Answer 14

The gravitational force obeys the inverse square law; if r increase by a factor of 2 then Fgrav will decrease by a factor of 2^2 = 4. Bigger distance, smaller force. If it is decreased by a factor of 2, the Fgrav will increase by a factor of 4.

Question 15

How can we find the gravitation acceleration?

Answer 15

mg = GMm^2/r^2 = g = GM/r^2

Question 16

Why is the value of g so much smaller on moon than earth?

Answer 16

The value of g on the moon is smaller bc the moon is much smaller than Earth(Mmoon «< MEarth), thereby exerting a smaller force.

Question 17

True or false. The normal force is always equal to the object’s weight.

Answer 17

FALSE. The normal force is the force that a surface exerts to keep itself intact (to keep you from falling into the ground or a wall). If you add an additional upward force to an object, then the normal force would be LESS than the weight.

Question 18

Define normal force.

Answer 18

A force that a surface exerts to keep itself intact. The Fn is the perpendicular component of the contact force exerted by a surface on an object.

Question 19

Give the equation for force of kinetic friction, and comment on its properties.

Answer 19

Ff = μk(Fnormal); note that it’s a scalar. Fn and Ff point in different directions. Use in SKIDDING or SLIDING. μk is typically less than μs.

Question 20

What’s the direction of kinetic friction?

Answer 20

The direction of the force of kinetic friction is always parallel to the surface and in the opp direction to the object’s velocity (relative to the surface).

Question 21

What is the direction of static friction?

Answer 21

The direction of static friction is always parallel to the surface and in the opp direction to the object’s intended velocity.

Question 22

On an inclined plane, the force of gravity acting paralell to the inclined plane = ___; the Fg acting perpendicular to the inclined plane = _____.

Answer 22

Fg parallel (x) = mgsinθ; Fg perpendicular (y) = mgcosθ

Question 23

Define center of Mass.

Answer 23

The point where the mass of an object is concentrated. It can be seen as a single particle. In some cases, the COM isn’t located within the body of the object. For a donut, the COM is in the center.

Question 24

Give the equation for COM.

Answer 24

Xcm =(m1x1 + m2x2 + m3x3)/ m1+m2+m3; x is the distance from a chosen origin.

Question 25

When solving the COM equations, what should you do first?

Answer 25

Choose an origin (reference point to call x = 0). The locations of the objects will be measured relative to this point. Often the easiest point would be the left hand mass but any point is fine. Should arrive at same answer.

Question 26

Why do people fall and how could we prevent it?

Answer 26

Falls occur when the COM of a person’s body is not located over a base of support (often determined by foot placement) and the person is unable to correct for imbalance. COM is determined by body shape and weight distribution. Hump = shifting COM forward. Obese = COM can shift out of base of support. Cane/walker would increase the size of the support base.

Question 27

Define Torque.

Answer 27

Torque is the measure of a force’s effectiveness at making an object spin or rotate ( at making an object accelerate rotationally). It is NOT a force in itself. It’s a property of a force.

Question 28

If an object is initially at rest, and then it suddenly starts spinning, what has occurred? If an object is already spinning, how do we get something to stop spinning?

Answer 28

An object at rest that suddenly starts spinning must have experienced a torque. Likewise, for a spinning object to stop, a torque must also be exerted.

Question 29

What is the equation for Torque.

Answer 29

T = rFsinθ [Nm]; θ is the angle between r and F. r is drawn from the pivot point to the pt of application.
T = l(F); the lever arm is the shortest distance from the pivot to the line along which F is applied, which is always perpendicular to line of action of F.

Question 30

What is the equation for Torque.

Answer 30

T = rFsinθ

Question 31

Define equilibrium. Define static equilibrium.

Answer 31

Eqilibrium = zero acceleration; doesn’t mean v = 0, v is constant. Static equilibrium = velocity is zero.

Question 32

Translational versus rotational equilibrium.

Answer 32

A sys is said to be in transitional eq if the forces cancel (Fnet = 0), then the translational acceleration is 0. A sys is in rotational eq if the torques cancel; if net torque = 0, then the rotational accerlation is zero.

Question 33

In torque equations, which direction is usually positive.

Answer 33

Counterclockwise is usually positive. Clockwise is negative.

Question 34

Force is assumed on act constantly over a distance. We say that the work done by the force is____.

Answer 34

W = Fdcosθ; θ is thge angle between F and d. If it’s perpendicular, it is 90 or 270, and cosθ = 0. Cos(0) = 1. Cos(180) = -1

Question 35

Is work a vector?

Answer 35

NO. Although work depends on two vectors for its definition (F and d), work itself is not a vector. W is a scalar. W may be positive, negative, or zero, but it has no direction. When adding total work for something, you can add the X and Y components.

Question 36

True or false. The total work done (found by adding up the values of the work done by each force separately) is always equal to the work done by the net force.

Answer 36

True.

Question 37

If θ is less than or equal to 90, work is ___.
If 90 < θ < 180, work is ____.
If θ = 90, then work is ____.

Answer 37

If θ is less than or equal to 90, work is positive.
If 90 < θ < 180, work is zero.
If θ = 90, then work is negative.

Question 38

True or false. Forces acting perpendicular to the direction of travel always do zero work.

Answer 38

True. On an inclined plane, gravity does work in the x-direction (mgsinθ) not (mgcosθ). mgcosθ is the normal force and will be used to calculate equations, however.

Question 39

When calculating work, what must stay consistent?

Answer 39

The formula W = Fdcosθ can only be used if the force is constant during the motion. If the force changes calculus is required. BUT, in a graph of force vs. position, assuming θ = 0, work done by the force is equal to the area under the curve.

Question 40

Power.

Answer 40

Power measures how fast work gets done. P = work/time = W/t.

Also, P = W/t = Fd/t = Fv, assuming F is parallel to d and that the object’s speed v, is constant.

W = Pt

Question 41

If you run for an hour on a horizontal treadmill, how much work did you do?

Answer 41

If you run for an hour on a horizontal treadmill, you have accomplished ZERO work. You’re not going anywhere. But obviously you burned a lot of calories.

Question 42

Kinetic energy. Meaning and equation.

Answer 42

Kinetic energy is the energy due to motion. Objects that move have the ability to do work since they crash into something and thus exert a force over a distance.

KE = 1/2mv^2 [J]; note that like work, KE is a scalar.

Question 43

There’s another way to calculate work other than Fdcosθ. What is it?

Answer 43

W(total) = ΔKE = KE(final) - KE(initial).

AKA the Work-Energy Theorem.

Question 44

When we’re pushing an object, energy is being transferred from ___ into the ___. When there is a force pulling in the opp direction from an object’s displacement, energy is being transferred from the ___ to the environment.

Answer 44

When we’re pushing an object, energy is being transferred from the environment into the object. + work implies a positive change in KE. When there is a force pulling in the opp direction from an object’s displacement, energy is being transferred from the object to the environment. Negative work = negative KE. If KE decreases, then so does the speed.

Question 45

Potential Energy.

Answer 45

Potential energy is the energy an object has by virtue of its position. It is the CHANGE in PE that is meaningful in physics.

Question 46

Is the work done by gravity positive or negative?

Answer 46

Work done by gravity is negative.

Question 47

The formula for potential energy.

Answer 47

ΔPE(gravity) = -W(done by gravity)

The change in gravitational PE is defined to be the opposite of work done by the gravitational force.

Question 48

ΔPE(gravity) = +mgh if the height of m is (increased/decreased) and -mgh if the high of m is (increased/decreased) by h.

Answer 48

ΔPE(gravity) = +mgh if the height of m is INCREASED and -mgh if the high of m is DECREASED by h.

Question 49

If an apple falls from the tree, the change in gravitational PE must be (positive/negative).

Answer 49

Negative.

Question 50

Explain why or why not gravity is a conservative force.

Answer 50

Gravity is a conservative force because the work done by gravity depends only on the initial and final heights or the object, NOT on the path the object follows.

Question 51

Explain why or why not friction is NOT a conservative force.

Answer 51

Friction is NOT a conservative force. If you have a triangle with points: A,B,C, and you go from A->B and A->C->B, more work must be done in the later situation. There is no such thing as “frictional PE” because PE can be defined only for conservative forces.

Question 52

What’s the equation for an object’s total mechanical energy?

Answer 52

E = KE + PE OR KE(i) + PE(i) = KE(f) + PE(f)

Question 53

Big 5 equations.

Answer 53

1) d = 1/2(v0 + v)t, missing a
2) v = v0 + at, missing d
3) d = v0t +1/2at^2, missing v
4) d = vt - 1/2at^2, missing v0
5) v^2 = v0^2 + 2ad, missing t

Question 54

Explain the principle behind the Conservation of Total Mechanical Energy.

Answer 54

If the only forces acting on an object during its motion are conservative ( ex., no friction), then the object’s total mechanical energy will remain the same throughout the motion. In other words, E(initial) = E(final).

Question 55

Let’s say an object is projected straight upward with an initial speed vo at time t = 0. How can we find the Total Mechanical energy and then the max height?

Answer 55

Use KE(i) + PE(i) = KE(f) + PE(f); Note PE(i) = 0 and KE(f) = 0. Think of this problem in terms of energy transformation. At the moment the object was shot upward, it only had KE; at the top of the path, however, it has only PE.

Question 56

Conservation of total Mechanical Energy (with outside/non-conservative forces).

Answer 56

KE(i) + PE(i) + W(by force= KE(f) + PE(f)

Question 57

The work required to move a brick to a height h is ___(the same/greater/less), regardless of whether you lift is straight upward or push it up a frictionless ramp.

Answer 57

The work required to move a brick to a height h is SAME, regardless of whether you lift is straight upward or push it up a frictionless ramp. Gravity is a conservative force. The force required to push up the ramp is less, however.

Question 58

Mechanical advantage.

Answer 58

How much less force is required when using a particular simple machine. MA = resistance force/effort force = F(resistance)/F(effort).

Can also be thought of as Force(out)/Force(in)

Question 59

Efficiency.

Answer 59

The efficiency of any machine measures the degree to which friction and other factors reduce the actual work output of the machine from its theoretical maximum.

Efficieny(%) = W(output)/Energy(input)