1. Kinematics and Dynamics

Question 1

When calculating the sum of vectors A and B (A+B), we put the tail of B at the tip of A. What would be the effect of reversing this order (B+A)?

Answer 1

There would be no effect.

Vector addition, unlike vector multiplication, is a commutative function. The resultant of A + B is the same as B + A, so there would be no difference between the two results.

If it were subtraction, or multiplication, there would be a difference.

Question 2

When calculating the difference of vectors A and B (A-B), we invert B and put the tail of this new vector at the tip of A. What would be the effect of reversing this order (B-A)?

Answer 2

It is oriented in the opposite direction

Vector subtraction, like vector multiplication, is not a commutative function. The resultant of A -B has the same magnitude as B-A but is oriented in the opposite direction.

Question 3

How is a scalar calculated from the product of two vectors?

How is a vector calculated?

Answer 3

A scalar is calculated from two vectors by using the dot product: A · B = |A| |B| cos θ.

A vector is calculated by using the cross product: A × B = |A| |B| sin θ.

Question 4

True or False: If C=A x B, where A is directed toward the right side of the page, and B is directed to the top of the page, then C is directed midway between A and B at a 45-degree angle.

Answer 4

False. This would be true of an addition problem in which both vectors have equal magnitude, but it is never true for vector multiplication. To find the direction of C, we must use the right-hand rule.

1. If the thumb points in the direction of A, and
2. the fingers point in the direction of B,
3. then our palm, C, points out of the page.

Question 5

What’s the difference between a scalar and a vector?

Answer 5

Vectors are physical quantities that have both magnitude and direction. Vector quantities include displacement, velocity, acceleration, and force, among others.

Scalars: Quantities without direction. Scalar quantities may be the magnitude of vectors, like speed, or may be dimensionless, like coefficients of friction.

Question 6

What is the right hand rule for multiplying two vectors?

Answer 6

1. Point your thumb in the direction of vector A
2. Extend your fingers in the direction of vector B
3. Your palm establishes the plane between the two vectors. The direction of your palm points is the direction of resultant C

Question 7

What is the relationship between instantaneous velocity and instantaneous speed? Between average velocity and average speed?

Answer 7

Instantaneous velocity and instantaneous speed are the same.

Average velocity and average speed may not necessarily be equal

Book: Instantaneous speed is the magnitude of the instantaneous velocity vector. Average speed and average velocity may be unrelated because speed does not depend on displacement but is rather the total distance traveled divided by time.

Question 8

True or false: the total distance traveled can never be less than the total displacement

Answer 8

Book: True. Displacement considers the most direct route between two points. Distance will always be equal to or larger in magnitude than displacement.

Question 9

Provide a definition for displacement or velocity in terms of another variable

Answer 9

Velocity is the rate of change of the displacement of an object.

Displacement is a function of velocity acting over a period of time.

Question 10

What is the difference between speed and velocity?

Answer 10

Speed: The rate at which an object covers a certain distance, cannot be zero or negative, and is a scalar quantity

Velocity: the rate at which an object changes positions in a certain direction, can be negative or zero, and is a vector

Question 11

How do you define a ‘force’?

Answer 11

A force (F) is any push or pull that has the potential to result in an acceleration.

This can be physical, like something you see, or something you can’t see (gravity, electrostatic force)

Question 12

How do you define gravity?

Answer 12

Gravity is the attractive force between two objects as a result of their masses.

Question 13

(Equation) What is the gravitational force equation?

Answer 13

It’s important to note that if one of the masses is triple, then the gravitational force will triple. If the distance changes, the force will change as an exponent of that distance change.

Question 14

How do you define friction?

Answer 14

Friction is a force that opposes motion as a function of electrostatic interactions at the surface of two objects.

Question 15

How do you define static friction vs kinetic friction?

Answer 15

Static friction (fs) exists between two objects that are not in motion relative to each other.

Kinetic friction exists between two objects that are in motion relative to each other.

Question 16

What will always be larger, the coefficient of static friction or the coefficient of kinetic friction?

Answer 16

the coefficient of static friction will always be larger than the coefficient of kinetic friction. It always requires more force to get an object to start sliding than it takes to keep an object sliding.

Question 17

(Equation) What is the equation of kinetic friction?

Answer 17

f_k= kinetic friction
μ_k= coefficient of kinetic friction
N= normal force

Normal force= m*g or n= mass x gravity

Question 18

What is the difference between mass and weight?

Answer 18

Mass is a measure of the inertia of an object- its amount of material. Mass is a Scalar quantity (no direction)

Weight is the force experienced by a given mass due to its gravitational attraction to the earth. Weight is a force, and is a vector quantity.

Question 19

(Equation) What is the equation for the force of gravity (or weight)?

Answer 19

F_g= mg

F_g= weight of the object
m= mass of object
g= acceleration due to gravity, 9.8 m/s^2 which is usually rounded to 10 m/s^2

Key concept: The center of mass of a uniform object is at the geometric center of the object (like a ball). However, keep in mind that most objects are not uniform (i.e. human, tennis racket, TV)

Question 20

What is acceleration?

Answer 20

Acceleration: is the vector representation of the change in velocity over time. Average or instantaneous acceleration may both be considered, similar to velocity.

Kahn Academy: Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.

Question 21

(Equation) What is the equation of average acceleration?

Answer 21

-

Question 22

When calculating frictional forces, how is directionality assigned?

Answer 22

The direction of the frictional force always opposes movement. Once the instantaneous velocity vector is known (or net force, in the case of static friction), the frictional force must be in the opposite direction.

Question 23

When no force is being applied, the velocity must be:

Answer 23

If there is no net force acting on an object, then that object is not experiencing acceleration and it has a constant velocity.

Question 24

True or False: the earth creates a larger force on you than you create on the Earth

Answer 24

False. Forces are always reciprocal in nature. When the Earth exerts a force on a person, the person also exerts a force of the same magnitude on the Earth (in the opposite direction). The difference in masses gives the Earth an apparent acceleration of zero.

Question 25

Name two forces in addition to mechanical manipulation (pushing or pulling forces created by contact with an object)

Answer 25

Gravity and frictional forces were discussed in this chapter. Electrostatic, magnetic, elastic, weak nuclear, and strong nuclear forces are other examples of forces.

Question 26

(Equation) what is newton’s first law of inertia?

Answer 26

states that an object will remain at rest or move with a constant velocity if there is no net force on the object.

F_net=ma=0

F_net= the net force
m= the mass
a= acceleration

Question 27

(Equation) what is Newtons’ second law of acceleration?

Answer 27

States that any acceleration is the result of the sum of the forces acting on the object and its mass. In other words, an object of mass m will accelerate when the vector sum of the forces results in some non-zero resultant force vector

F_net=ma

F_net= the net force
m= the mass
a= acceleration

Question 28

(Equation) What is Newton’s third law of acceleration?

Answer 28

Newton’s third law states that any two objects interacting with one another experience equal and opposite forces as a result of their interaction. In other words, to every action, there is always an opposed but equal reaction

F_AB= -F_BA

Question 29

During a test crash, a 500 kg car is driven at a constant velocity of 50 mph until it hits a wall without braking. Apply all three of Newton’s Laws to this situation

Answer 29

1.Prior to the collision, the vehicle is travelling at constant velocity, which (according to Newton’s first law) indicates that there is no acceleration and no net force.

2. The collision with the wall creates a sudden deceleration. Because there is acceleration, there must be a net force. The value of the net force can be calculated by multiplying the mass of the car times the acceleration.

3.When the car collides with the wall, the car exerts a force on the wall. Simultaneously, the wall exerts a force of equal magnitude in the opposite direction on the car.

1. states that an object will remain at rest or move with a constant velocity if there is no net force on the object.
   2.States that any acceleration is the result of the sum of the forces acting on the object and its mass. In other words, an object of mass m will accelerate when the vector sum of the forces results in some non-zero resultant force vector
   3.Newton’s third law states that any two objects interacting with one another experience equal and opposite forces as a result of their interaction. In other words, to every action, there is always an opposed but equal reaction

Question 30

(Equation) What is the equation to find velocity?

To find Velocity (no displacement)

Answer 30

v=v_o + at

V= velocity
v_o= is the initial velocity
t= time (seconds)
a= acceleration

acceleration= due to gravity, 9.8 m/s^2 which is usually rounded to 10 m/s^2

Question 31

(Equation) What is the equation used to find position from velocity?

To find Position (no final velocity)

Answer 31

Equation #3

Δx=v_ot + (1/2)at²

y= distance in the y direction
v_o= is the initial velocity
t= time
a= acceleration due to gravity, 9.8 m/s^2 which is usually rounded to 10 m/s^2
t= time

Question 31

(Equation) What is the equation used to find position from velocity?

To find maximum height when something is thrown (no time):

Answer 31

v²=v_o² + 2aΔx

v= final velocity (may be 0)
v_o= is the initial velocity
a= acceleration due to gravity, 9.8 m/s^2 which is usually rounded to 10 m/s^2
y= distance

Question 32

What must you do with projectile motion problems?

Answer 32

You must evaluate the x- and y- component separately.

Question 33

(Equation) in inclined plane equations, what is the force that is parallel to the ramp?

What is the force that is perpendicular to the ramp?

Answer 33

F_g∥=mg sin⁡θ (force parallel to the ramp)
F_g⊥=mg cos⁡θ (force perpendicular to the ramp)

F_g∥= the component of gravity parallel to the plane (oriented down
F_g⊥= component of gravity perpendicular to the plane
m= mass
g= acceleration due to gravity (9.8 m/s²)
θ= angle of the incline

Question 34

(Equation) What is the equation of circular motion, or centripetal force?

Answer 34

F_c= magnitude of centripetal force
m= mass
v= speed
r= radius of the circular path

In centripetal force problems, even though there is constant velocity, there is acceleration, because the object is constantly changing position (it’s moving in a circle).

Question 35

How do the forces acting in free fall and projectile motion differ?

Answer 35

Both free fall and projectile motion both have a y component that brings an object down.
However, projectile motion also has an x-component, that moves it in a direction

Book: The only force acting in both free fall and projectile motion is gravity.

Question 36

At what angle of launch is a projectile going to have the greatest horizontal displacement? What angle will result in the greatest vertical displacement, assuming a level surface?

Answer 36

The product of sin and cosine is maximized when the angle is 45°. Because horizontal displacement relies on both measurements, the maximum horizontal displacement will also be achieved at this angle.

It will have the greatest vertical displacement at a 90-degree angle.
Book Vertical displacement will always be zero as the object returns to the starting point. Objects launched vertically will experience the greatest vertical distance.

Question 37

How would you define the topic of dynamics?

Answer 37

The study of torques and force

Question 38

What are free body diagrams?

Answer 38

Free body diagrams are representations of the forces acting on an object. They are useful for equilibrium and dynamic problems.

MCAT Expertise: when dealing with dynamics questions, always draw a quick picture of what is happening in the problem; this will keep everything in its proper relative position and help prevent you from making simple mistakes.

Question 39

What is rotational equilibrium?

Answer 39

Rotational equilibrium occurs in the absence of any net torques acting on an object. Rotational motion may consider any pivot point, but the center of mass is most common. An object in rotational equilibrium has a constant angular velocity; on the MCAT, the angular velocity is usually zero.

Google: Rotational Equilibrium An object is in rotational equilibrium (its angular momentum is constant) if the sum of the torques acting on it is zero. An object will be in equilibrium if it is suspended from its center of gravity or its center of gravity is below the suspension point.

Translational equilibrium is absence of net acceleration.

Angular Velocity: time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes

Question 40

What is translational equilibrium?

Answer 40

Translational equilibrium occurs in the absence of any net forces acting on an object. An object in translational equilibrium has a constant velocity and may or may not also be in rotational equilibrium.

Bjueys: A mass or an object is in translational equilibrium when the sum of all the external forces acting on the object equals zero it means an object is in translational equilibrium when overall acceleration is zero . Therefore, it is either not moving or moving at a constant velocity.

Rotational acceleration is absence of net torque

Question 41

(Equation) What is the equation to find the torque?

Answer 41

τ = r × F = rF sin θ

τ= torque
r= the length of the lever arm
f= magnitude of the force (mass + gravity or mass x 9.8)
θ= then angle between the lever and force vectors

Question 42

What is the notation (positive or negative) for torques that are going clockwise and counterclockwise?

Answer 42

clockwise rotation are negative

counterclockwise are positive

Question 43

Can a moving object be in equilibrium? Why or why not?

Answer 43

Yes, it can, as long as the acceleration is 0

Book: A moving object can be in either translational or rotational equilibrium (or both). Translational equilibrium only requires the net force on an object be zero—its velocity is constant. The corresponding condition in rotational equilibrium is that net torque equals zero—its angular velocity is constant.

Question 44

If you have an object three times as heavy as you can lift, how could a lever be used to lift the object? Where would the fulcrum need to be placed?

Answer 44

τ = r × F
r x mg (which equals force) = r mg (3)

The distance would be three times the length away from the fulcrum as you are.

One could place the fulcrum one quarter of the way across the lever, closer to the object. The ratio of the lever arms would then be 3:1, which means that only one-third of the original force is necessary. (Alternatively, the fulcrum could be placed at the end with the object one-third of the way across the lever. This would again result in a 3:1 ratio of lever arms, meaning that only one-third of the original force is necessary.)

Question 45

What is the normal force?

Answer 45

The normal force is the force that surfaces exert to prevent solid objects from passing through each other. Normal force is a contact force. If two surfaces are not in contact, they can’t exert a normal force on each other.