kinematics (ch.3)
Which of the following kinematic descriptions is physically impossible? A. An object in motion for some period of time has zero average velocity but positive average speed. B. An object maintains constant speed but has nonzero acceleration. C. An object in motion has zero displacement but positive total distance traveled. D. An object in motion for some period of time has an average velocity with a greater magnitude than its average speed
- Choices A and C are both possible because an object traveling in a closed curved path (like a circle) will have zero displacement and therefore zero average velocity but not zero distance or average speed. - Choice B is possible, because it is the case for uniform circular motion. - Average velocity has magnitude of displacement / time, whereas average speed equals total distance / time. The time is the same for both, and displacement ≤ total distance, so average velocity ≤ average speed. Put another way, there's no shorter path than a straight line, for which the magnitude of displacement equals the total distance. For any other type of path, the displacement is shorter than the distance traveled.
acceleration and velocity
- if acceleration is positive, which means it points to the right, just like Vi. If the acceleration points in the same direction as the initial velocity, then the object's speed is INCREASING (i.e. both a and vi are negative = object's speed is increasing; both a and vi are positive = object's speed is increasing) - if acceleration is negative, which means that it points to the left and is in opposite direction to Vi. If the acceleration points in the direction opposite to the initial velocity, then the object's speed is DECREASING - if acceleration is perpendicular to velocity, means object's speed is constant
speed
- the magnitude of the velocity vector - Speed is Scalar = it has no direction and can never be negative (ex: 5 m/s)
uniformly accelerated motion
- the object's acceleration is constant (i.e. free fall = an object is moving only under the influence of gravity) - Use the big 5 equations
position vs. time graph
- the slope of a position vs. time graph gives the velocity
velocity vs. time graph
- the slope of a velocity vs. time graph gives the acceleration - the area under a velocity vs. time graph gives the displacement
tera
10^12 610THz = 610x10^12 Hz
if an object is accelerating then it must be: A.changing its velocity. B. increasing its speed. C. changing its direction. D. traveling in a straight line.
= changing its velocity - By definition, acceleration implies a change in velocity. ("Changing its direction" is wrong because an object can accelerate without changing its direction [just drive in a straight line and step on the gas]. "Traveling in a straight line" and "increasing its speed" are wrong because an a turning object moving at constant speed is constantly accelerating.)
An object is moving along a one-dimensional path. At its turning point: A. the acceleration is zero. B. the instantaneous velocity is zero. C. all of these statements are true. D. the average velocity of the object is zero
B
displacement
Distance and direction of an object's change in position from the starting point. (ex: 5m to the north)
giga-
G 10^9
A block of mass m begins to slide down a vertical wall. If the wall is frictionless, what minimum horizontal force F must be applied to the block to keep it from sliding any further? (g = magnitude of gravitational acceleration) A. No horizontal force, however strong, can keep the block from sliding down the wall. B. F = 3mg C. F = 2mg D. F = mg
If the wall is frictionless, no horizontal force, however strong, can keep the block from sliding down the wall. If the wall is frictionless, then there is no vertical force to oppose the downward force of gravity on the block. (This is because Ffriction = µN = µF but µ = 0, so Ffriction = 0). Therefore, regardless of how great the "pressing" force F is, the block will slide down the frictionless wall.
mega-
M 10^6
velocity
how fast an object's position changes - Velocity is a Vector = that specifies both speed and direction (ex: 5 m/s to the north) - if two velocities are the same = the direction and the speed are the same - if cars have same speed but different velocities = means direction is different
acceleration
how fast an object's velocity changes - an object can be accelerating even if the speed is constant - cruise control set at 60 mi/hr (speed is constant) but you turn wheel as you approach curve (direction changes) = velocity vector changes and you experience an acceleration
kilo-
k 10^3
milli-
m 10^-3
nano-
n 10^-9
displacement
object's change in position - is a vector and takes direction into account ( a negative sign may be indicative of the left direction)
pico-
p 10^-12
density
p kg/m^3 M/L^3 (meters over length cubed)
kinematics
study of motion in terms of an object's position, velocity, and acceleration
centi-
c 10^-2
Which of the following best describes the motion of a body along a surface where friction must be taken into account? A. Less force is required to start the object in motion than to keep it in motion at constant velocity. B. The same force is required to start the object in motion as to keep it in motion at constant velocity. C. More force is required to start the object in motion than to keep it in motion at constant velocity. Correct Answer D. Once the object is set in motion, no force is required to keep it in motion at constant velocity.
More force is required to start the object in motion than to keep it in motion at constant velocity best describes the motion of a body along a surface where friction must be taken into account. For the vast majority of surfaces, the coefficient of static friction is greater than the coefficient of kinetic friction. Thus, the maximum force that static friction can withstand is greater than the force that kinetic friction will exert as the object slides. This directly implies the statement in the correct answer, "more force is required to start the object in motion than to keep it in motion at constant velocity."
An object accelerates uniformly from rest and moves a distance X meters in time T seconds. If the object accelerates uniformly from rest with the same acceleration, how far does it move in time 2T seconds? A. (1.4)X meters B. 2X meters C. 4X meters D. Impossible to determine with the given information.
The first sentence gives the variables d, v0, and t, and from this we could find either a or v. One option would be to solve for a and use that with the information given in the second sentence to find d for t = 2T. However, it is more efficient simply to note that with v0 = 0, d ∝ t2, since d = v0t + 0.5at2. Hence, if time doubles (with all other conditions being equal), distance must quadruple.
work
W kg*m^2/s^2 ML^2/T^2 (meters x length squared over time squared)
During a rainstorm, you notice that the raindrops are not always the same size: some are small, others are larger. Raindrops fall with a constant velocity (called their terminal velocity). Given that the upward force of air resistance is proportional to the speed of the falling drop, which raindrops—the smaller ones or the larger ones—fall with the greater speed? A. The smaller drops, since the force of air resistance on them is smaller. B. The larger drops, since they acquire greater speed before air resistance eventually balances out the force of gravity. C. The smaller drops, since their smaller mass gives them greater acceleration. D. Neither; even taking air resistance into account, they fall at the same speed
the larger drops will fall with the greater speed, since they acquire greater speed before air resistance eventually balances out the force of gravity. Since raindrops fall with constant velocity, their acceleration is 0, so the net force on each drop must be zero also. Therefore, the upward force of air resistance must eventually balance the weight of the drop. Since larger drops weigh more, the force of air resistance they feel must be greater than for smaller drops. But greater air resistance FR must be due to a greater speed (since FR : v). Therefore, larger drops fall with greater speed than smaller ones do.
projectile motion
the motion of the object, experiencing only the constant, downward acceleration due to gravity (free fall) - projectile is experiencing both horizontal and vertical motion - use big 5 to look at horizontal motion and vertical (separately) AT THE TOP OF THE TRAJECTORY - vy = 0 - vx is not equal to zero - initial velocity in the y-direction at beginning = -initial velocity in y direction **projectile motion is 2D near Earth's surface that ignores all effects but gravity *if question states initial velocity is in the x-dir then vy=0; cannot be both*
An object moves along a flat, horizontal surface. An applied force of 100 N points to the right and the force of kinetic friction is 300 N and points to the left. Which of the following is true? A. The object is not moving. B. The object moves to the left. C. The object first moves to the right, then changes direction and moves to the left. D. The object moves to right and is slowing down
the object moves to right and is slowing down. The problem states that the object is moving, so we can eliminate the choice stating the object is not moving. The force of kinetic friction points to the left. Since kinetic friction is always directed opposite the motion, the object must be moving to the right. Since friction is greater than the applied force, the object is accelerating in a direction opposite the motion. Therefore the object is slowing down. Eventually the object will stop and the friction will become static friction, keeping the object motionless.
A common Christmas ornament is a thin string passed through a long sequence of popcorn pieces. If such a string is allowed to hang vertically from the ceiling and does not touch the ground, what best describes the tension in the string? (Assume the string is massless but the popcorn is not.) A. The tension is uniform throughout the string, or the string would pull itself apart. B. The tension is greatest in the middle, because that segment of string has an equal weight of popcorn above it (weighing it down) and below it (pulling down on it). C. The tension is greatest at the bottom just before the final popcorn kernel, because that segment of string has all of the mass of popcorn above it pushing down on it. D. The tension is greatest where the string attaches to the ceiling, because that segment of string is supporting the greatest weight.
the tension is greatest where the string attaches to the ceiling, because that segment of string is supporting the greatest weight. The tension in any segment of string must support (i.e., cancel out) the weight of the popcorn below it, according to Newton's first law. Therefore the segment of string that has the greatest weight below it, the topmost segment, must have the greatest tension. If the string were pulled taut horizontally, then it would have the same tension throughout (at least to a rough approximation applicable on the MCAT). Note that strings don't push, so the weight above any segment is not relevant to the determination of tension.
micro-
u 10^-6
speed
v (velocity) m/s L/T (length over time)
