Forces

Question 1

As Juan walks by your desk, he flicks the ruler at angle. This force is applied away from the center of mass. What are the expected results?

Answer 1

The ruler will rotate about its center of mass

Question 2

In order for a mass to rotate about its normal center of mass when a force is applied to part of it away from the center of mass, what assumption must be made?

Answer 2

The object has to be an untethered, free floating object

Question 3

You nail a ruler midway into the wall at the 4 inch mark. What has changed about its center or mass.

Answer 3

The center of mass of around 6 inches has shifted to the 4 inch mark. Tethering it creates a pivot point (which becomes the axis at which it rotates about

Question 4

As you flick the nailed ruler at the edge, what do you expect to happen? How is this different from flicking the ruler at the same point if it was not hanging and just sitting on your desk.

Answer 4

The ruler would rotate about the nailed portion. If the nail was not tethered, it would rotate about its geometric center, around the 6 inch mark.

Question 5

True or False - The Force in Torque is the force in which the object creates.

Answer 5

False, this is the applied force to the object at 90 degree angles. D - is the distance at which the 90 degree angle force is applied to the object away from its pivot point.

Question 6

True or False - Torque is a force at which increases or decreases the object’s rotational motion.

Answer 6

True

Question 7

Torque: 
N 
N*m
J
J*m

Answer 7

Nm Torque = Force * Distance. Though Joules can be converted into Nm, torque is not a work (measured in joules). Therefore must specify the units for torque

Question 8

True/False Torque is measured in Nm and Nm can be converted into Joules (a measurement of Work) Therefore Torque is work.

Answer 8

False, Torque is not a type of energy rather, a type of force.

Question 9

Your lamp on your desk is hinged in the center. Desperate to study in the dark room, you push on the handle of the lamp with 5 Newtons, 10 cm away from the hinge at a 90 degree angle. How much torque is created?

Answer 9

T = F*m

= 5N * 10 e-2m = 50 x 10-2 N*m

Question 10

How to know if the torque is positive or negative

Answer 10

Counterclockwise - Positive

Clockwise - Negative

Question 11

As you apply a 5 x10-2 N*m Torque on your lamp at a 90 degree angle, the lamp comes to a stop as it bumps into a pencil 5 cm from the axis of rotation. The pencil is also pushing up at the lamp handle at a 90 degree angle. What is the net torque in this scenario? How much force is the pencil applying up?

Answer 11

Net Torque = 0 = T 1 + T 2
5x10-3 N*m + T 2 = Net Torque
Torque 2 = -5x10-2 N*m
T = F *d = -5x10-2 N*m = F * (5cm) 
=> F = 1 N

Question 12

What is mechanical advantage? How is this concept relevant to the concept of torques and forces of a rotating object?

Answer 12

Mechanical advantage is the ratio of force produced by a machine to the force applied to it. By using a machine that has the ability to produce torque, you can decrease the amount of force inputted into the system.

Question 13

Much like linear or translational acceleration, how is angular acceleration similar?

Answer 13

α=ΔωΔt α = Δ ω Δ t , where Δω is the change in angular velocity and Δt is the change in time

Question 14

How is angular velocity related to position?

Answer 14

You can find the a angular velocity by taking the change in angular position over time
=> Δθ/t

Question 15

What creates angular or rotational motion?

Answer 15

Much like how a net force is required to create a translational motion, a net force, called torque, is required to act on the object to cause pivoting of the object about the axis

Question 16

Is Force the only thing that affects the angular motion?

Answer 16

No, distance at which the force acts on the object away from its center of mass also plays a role AKA the lever arm. Both create the torque

Question 17

Q - A door is attached to a hinge and as the door opens or closes, the door rotates around the hinge. The hinge acts as all of the following except: 
A. Angular Position
B. Axis of rotation
C. Fixed Axis
D. Center of mass

Answer 17

A. Angular position. Angular position/location takes account of the axis of rotation. This is the angle at which the line of reference rotates with the object relative to the axis. All other answers are correct and C is correct so long as the axis doesn’t move.

Question 18

Alex is chasing Angelie and she runs into a room and attempts to slam it shut, however Alex quickly shoves against it and it doesn’t close all the way. Alex pushes near the door knob while Angelie is pushing against the door closer to the hinge. What is the ultimate result if both of the forces applied are the same?

Answer 18

The location at which you apply force in these scenarios matter. Net forces applied closer to the hinge or the axis of rotation creates a smaller angular acceleration compared to the applied force further from the fixed axis. This is due to the lever arm - this is the distance from the axis of rotation perpendicular to the line along which the force acts. Therefore, Alex will overpower her and be able to enter the door.

Question 19

Compare and contrast F|| and F⊥ in terms of angular rotation.

Answer 19

F⊥ = Fsinθ while F|| =Fcosθ. F|| is the parallel force applied to the object parallel to the axis of rotation and F⊥ is the perpendicular force applied to the object perpendicular to the axis of rotation.

Question 20

The line which is perpendicular to the lever arm as an object moves about an axis of rotation is:
A. The line of Acceleration
B. The line of Force
C. The line of Rotation
D. The line of Centripetal Acceleration

Answer 20

B. The line of force. The line of force acts in the same direction as the applied force (this is the direction of the force basically)

Question 21

Torque: 
A. J/m
B. N/m
C. N
D. N*m

Answer 21

D. Torque is the force acting on an object to cause rotation of the object. Units are N*m

Question 22

What is a requirement for torque to occur? How does this help identify the mathematical expression of torque?

Answer 22

The force applied to the object has to be anywehere from parallel to perpendicular to the axis of rotation. Therefore it can not be parallel to the axis of rotation. Therefore you have to use F⊥ = Fsinθ => τ = rF⊥ => τ = rFsinθ, where r = radius (meters)

Question 23

In an experiment, you place a small disk on top of a larger disk by drilling a hole in the middle and connecting the two with a hinge at the center, allowing both disks so they move as one. You apply a force (F1) at a 60 degree angle with respect to the x axis to the y axis and another force (F2) at a 30 degrees to the y axis to the smaller disk. What is the overall motion?

Answer 23

Lever arm for F2 is R2 because R2 is perpendicular to the force. There is no motion overall.

Question 24

In an experiment to determine which object moves the fastest down a ramp, you place a ring, box, and a ball on the top. Do they all reach the ground at the same time?

Answer 24

No. This is due to how the energy is distributed in an object when it is rolling down, causing each object to have a different overall speed.

Question 25

In a vacuum, you drop a feather and bowling ball at the same time from the same height. Why do they both reach the floor at the same time? Why is this different from the experiment of objects (ring, ball, and block) moving down on a ramp?

Answer 25

From a height with no other forces (such as gravity) acting on the two objects, the energy of potential is completely converted to kinetic energy and therefore they PE = KE and both have the same translational KE. In a ramp, all the potential energy is not exactly converted to the KE of the object. For objects that have the ability to rotate, some energy will be converted into angular KE as well.

Question 26

True or False: In calculating the torque of an object, the angle of focus is between the lever arm and the axis parallel to the axis of rotation

Answer 26

True. The angle of interest is the angle between the applied force and the radius

Question 27

Net torque can be summed as what else as well?

Answer 27

Tnet = αI 
α = angular acceleration 
I = moment of inertia

Question 28

Moment of inertia of an object is …

Answer 28

This is the tendency of an object to keep doing what it is currently doing. The sum of all indv points of mass in an object at a distance from the center of mass
I = Σmr^2

Question 29

Two objects of the same masses sit at different radii from the center of mass. Which one object has more inertia?

Answer 29

I = ∫r^2dm AKA mr^2| r = radius and m = mass. Therefore, the bigger the radius/mass, the more inertia an object has

Question 30

Describe the relationship between work and torque.

Answer 30

Torque has the ability to do work. The work done by torque is the integral of the torque over a certain angle. Therefore the more torque you apply while rotating an object, the more work you do

Question 31

Describe the relationship in between rotational Kinetic Energy and inertia. How is it similar to translational kinetic energy?

Answer 31

KE rotational = 1/2Iω^2

Both have the ½(variable)variable^2

Question 32

Describe the relationship of momentum and kinetic energy. How is this seen in kinetic energy?

Answer 32

The mathematical expressions of both kinetic energy and momentum encompass multiplication of the same variables. In angular motion, momentum (L) = Iω while the angular kinetic energy is the elaboration on the angular momentum- (KErotation) = 1/2Iω^2

Question 33

For objects that have the ability to rotate, what happens to the conversion of its potential energy if it was let go from a hill?

Answer 33

The potential energy is converted to not only translational kinetic energy, but also rotational kinetic energy. Therefore PE = KEtranslational + KErotational

Question 34

Does a higher moment of inertia have the ability to have more velocity. Utilize a circular object and a block moving down a ramp as your example

Answer 34

Though the inertia is defined as mass of object*radius^2, the translational kinetic energy of a moving object is not always dependent on inertia. This angular kinetic energy describes the motion of the mass rotating about its center, which does not have anything to do with translational motion and therefore velocity

Question 35

True or false: Net force is sometimes called the term to define an overall unbalanced force

Answer 35

True

Question 36

On a macroscopic level the normal force and gravitational force on an object on the floor are called…. What are they called at a microscopic level?

Answer 36

Contact forces. On a microscopic level, these forces are simply electromagnetic repulsion as a result of electrons repelling on neighboring atoms

Question 37

What phenomenon exists to act out normal forces on a microscopic level?

Answer 37

Electromagnetic Repulsion. Electrons of atoms repel against one another on the surface allowing the normal force to exist

Question 38

Say that Angelie steps onto an elevator and doesn’t do much but stand there. If she weighs 10kg, how much is the normal force of the elevator acting onto her?

Answer 38

No acceleration of the elevator, therefore this scenario is following just Newton’s first law.
Force of gravity = mg = 10kg-9.8m/s^2 = -98 kg*m/s
F normal = 98 kgm/s

Question 39

You step onto an elevator to go to your med school interview. You click the button and the elevator starts to accelerate at 2 m/s^2. If you weigh 60 kg, how much normal force is acting on you as you ascend.

Answer 39

S1: Newton’s Second Law (Force due to gravity) : F = mg = 60kg9.8m/s^2 ~ 600 N
S2: Newton’s Second Law (Force due to acceleration) : F = ma = 60kg2m^2 = 120 N
S3: Summation of both laws: 600 N + 120N ~ 720 N normal force and -720 force due to gravity

Question 40

As Angelie ascends in an elevator, the elevator starts to move at a constant acceleration with a velocity of 10m/s. What is the net force acting onto her as she stands.

Answer 40

Even though there is a velocity, the acceleration is constant. At a constant velocity, there is no net force (Newton’s first law)

Question 41

What is the normal force acting on you (60kg) as you are reaching your floor and the elevator starts to decelerate at -2m/s^2 as it ascends?

Answer 41

Newton’s second law (force due to acceleration of object): F = ma = 60kg-2m/s^2 = -120 N upwards
Newton’s second law (Force due to gravity): F = mg = 60kg9.8m/s^2 ~ 600 N
Combine the two laws: 600N + (-120N) = 480 N of normal force to counter the force of gravity, therefore you are feeling like you are moving down.

Question 42

Johnny gets on the elevator. He has a mass of 103.54kg (too many sweets, Johnny). The elevator starts accelerating upwards at 2.13 m/s^2. What is the normal force acting on Johnny (in N)?
A. 786.34
B. 942.01
C. 1235.23
D. 1654.90

Answer 42

Acceleration means the force is acting per Newton’s second law - F = ma
F due to acceleration = 103.54kg2.13m/s^2 = 220.54 N
Force of gravity = mg = 103.54kg9.8m/s^2 = 1014.692 N
Net force = Force of Gravity + Force of acceleration = 220.54N + 1014.692N = 1235.23 N downward

C. 1235.23 N upwards

Question 43

In Physics, how do we mathematically define weight?

Answer 43

F = m*g This is also the force due to gravity/force by gravity/force of gravity/etc… because this is the amount Newton’s gravity has on one’s mass.

Question 44

True or false: Newton’s third law outlines that the normal force seen from the surface acting onto an object is the reaction force to the action force gravity.

Answer 44

False. The forces entailed by Newton is specifically talking about forces acting on different objects. Ex: ground creates force on ball (object # 1) in upwards direction while the ball creates a force onto the ground (object #2) in downwards direction

Normal force is the force onto the ball from the ground in response to gravity onto the ball, therefore the two forces act on the same object.

Question 45

Find the normal force and the weight of a box lying on a table if the box has a mass of 25kg

Answer 45

No acceleration means that forces acting on the box causes the box to have no acceleration in any dimensions
Force due to gravity AKA weight of the object = mg = 25kg-9.8m/s^2 = -245N
Therefore Normal force = 245 N
ε F = Fn - Fg = 0

Question 46

Catalina decides to push down on the box at 50 newtons in an attempt to crush it, however it does not budge. Find the normal force and the weight of the object

Answer 46

No acceleration means => ε F = Fn - Fg - F = 0

Fn = Fg + F = 245N + 50N = 295N

Question 47

Frustrated at Catalina, Juan grabs the box and lifts it directly upwards with a force of 70 N. Find the normal force.

Answer 47

Assume there is no acceleration because not explicitly stated. ε F = Fn - Fg + F =0
Fn = Fg - F = 245N - 70N = 175N
The normal force is not always equal to the weight!!!

Question 48

What is the acceleration of a round weight of 10kg if Michael decides to lift it directly up with a force of 110N. Will the box move?

Answer 48

F = Full - Gravity = ma
110N - 10kg9.8m/s^2 = 10kg*a
a = (110-98)/100 = 1.2m/s^2 up

Question 49

Say there is a block of ice sitting on a frozen lake. What are the forces acting on this block? Are they equal?

Answer 49

Force of Gravity - Downward force. Normal Force - Prevents acceleration going down, and points up.
Fnet = Fn + Fg =0

Question 50

A vacuum-like planet named Persi I-8 has just undergone an ice age and the surface of the planet is completely covered in an even layer of ice. If a block of ice escaped and was traveling in a steady velocity, what are the forces acting on this block? Are the forces equal?

Answer 50

In this case, if the Fnormal and Fg are equal in magnitude but differ signs, they would cancel out and there will be no net force and the object would not accelerate in any direction. Therefore the block would continuously travel and leave the planet itself. But it ends up orbiting the plant instead!

Due to this circular pathway, it is constantly being accelerated inward. Therefore there is some inward centripetal acceleration occurring and therefore the net inward force must be greater than the magnitude of the normal force.

Question 51

An internal force that exists within the object and counters another force is..
A. Tension 
B. Normal Force
C. Gravity
D. Reaction Force

Answer 51

A. Tension force - This force exists is usually seen when lifting or pulling an object ans is innate to a wire or string

Question 52

Juan suspends a 100N weight from the ceiling. How is the weight able to achieve this if gravity is causing a downwards force on it?

Answer 52

Downward force due to gravity = 100 N, however the weight is not accelerating. Therefore there is another force counteracting the force of gravity. This is achieved by the wire/string and the force the wire produces called tension. This tension offsets the force of gravity and should have tension of 100 N in upwards

Question 53

True or False: Cos30 and sin60 = ½

Answer 53

False. Cos30 and sin 60 = sqrt(3)/2. Meanwhile cos60 and sin 30 = 1/2

Question 54

True or false: Cos 60 and sin 30 = sqrt(3)/2

Answer 54

True!! Meanwhile cos60 and sin 30 = 1/2

Question 55

1 g in physics is measured as…

Answer 55

1 force of gravity AKA 9.8 m/s^2. Therefore is you are traveling 2 g, you are traveling at ~20 ms^2

Question 56

In discussing inclines in physics, what does it really imply?

Answer 56

It implies ramps are in discussions.

Question 57

When dealing with inclined planes, how are the axes defined?

Answer 57

X axis - along the ramp

Y axis - perpendicular to the ramp

Question 58

Θ is the angle used to define what in problems with inclined planes? Where else is this angle shared?

Answer 58

Theta (Θ ) is the angle of the incline plane with respect to the ground. Theta is the same as the angle in between the Fg and Fn and both share the same magnitude

Question 59

On an incline plane, an object is slowly sliding down the ramp. What is the mathematical expression to describe this force?

Answer 59

sinθFg = mg(sinθ)

Question 60

As Angelie sits on top of a slide, she slips down along the playground. How do we define the normal force acting on her?

Answer 60

The normal force is the force acting onto her, perpendicular to the surface of the slide. cosθFg = mg*cosθ

Question 61

What is the mathematical acceleration of a box as it slides down the ramp?

Answer 61

g*sinθ, slightly less than our g

Question 62

A box with mass 20 kg, slides down a frictionless plane with an angle of 30 degrees with respect to the ground. Find the acceleration of this box

Answer 62

Magnitude of acceleration = g sintheta (because it points in the direction of the plane)
sin(3)9.8 = ½(9.8) = 4.9 m/s^2

Question 63

A box with mass 20 kg, slides down a frictionless plane with an angle of 30 degrees with respect to the ground. Determine the normal force on the box.

Answer 63

Fn = costheta*mg = cos30 * 9.8 = 170N is exerted on our box directly perpendicular along the y axis (and to the incline plane)