Physics Toolkit
Draw an example of a set of results that illustrate high precision but low accuracy.
Figure should show points clustered close together but far from the true value.
Which of the following is NOT a vector?
(A) Position
(B) Distance
(C) Velocity
(D) Acceleration
(B) Distance
distance does NOT have a direction
Displacement can be obtained from:
A) the slope of an acceleration-time graph
B) the slope of a velocity-time graph
C) the area under an acceleration-time graph
D) the area under a velocity-time graph
E) the slope of an acceleration-time graph
D) the area under a velocity-time graph
If you drop a rock and a feather, the rock hits the ground first. This demonstrates that:
A) The acceleration of gravity is not constant.
B) Heavier objects are accelerated faster by gravity than lighter objects are.
C) Air resistance has a larger effect on feathers than on rocks.
D) Rocks can’t fly.
E) Gravity has little effect on a feather.
C) Air resistance has a larger effect on feathers than on rocks.
A book is being pushed against the side of a bookcase with a force of 2 N. What is the force and direction that the bookcase exerts on the book?
2 N in the opposite direction
Which of the following is a systematic measurement error?
(A) Consistently measuring from the end of a ruler that doesn’t start at zero
(B) Timing an event with a stopwatch, where you sometimes stop the watch too soon and sometimes too late
(C) Using the wrong equation(s) in your calculations
(A) Consistently measuring from the end of a ruler that doesn’t start at zero
A physics students walks halfway to school, realizes she forget her homework, walks back home, then walks from home to school. The distance between her home and school is 0.5 miles.
What distance did she travel?
Distance = 1.0 mile
Distance = total path length = 0.25 + 0.25 + 0.5
The position vs. time graph of an object is a straight line with a positive slope. The object has:
A) constant displacement
B) steadily increasing acceleration
C) steadily decreasing acceleration
D) constant velocity
E) steadily increasing velocity
D) constant velocity
Two cannonballs are launched:
(A) has an initial velocity of 25 m/s at an angle of 45 deg
(B) has an initial velocity of 15 m/s at an angle of 55 deg.
Which one spends longer in the air?
(A): 25sin(45) > 15sin(55)
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Longer time = larger initial vertical velocity
v2y = v1y + at --> v2y = 0 at top, time up = time down, so 0 = v1y - 9.8t --> t = v1y/9.8
v1y = v1sin(theta)
Two forces are acting on an object that is in equilibrium. F1 = 20 N at 30 deg. F2 = 30 N at 155 deg.
What is the magnitude and direction of F3?
F3 = 24.7 N @ -66.5 deg (OR 293.5 deg)
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x-direction: 20cos30 + 30cos155 + F3x = 0
y-direction: 20sin30 + 30sin155 + F3y = 0
F3x = 9.87 N, F3y = -22.68 N
F3 = sqrt(9.87^2 + (-22.68)^2) = 24.73 N
theta = tan-1(-22.68/9.87) = -66.48 deg
Doing more trials:
(A) Improves accuracy but not precision
(B) Improves precision but not accuracy
(C) Improves both accuracy and precision
(D) Improves neither
Either (A) or (D):
- More trials does NOT precision (if you have a lot of scatter in your measurements, doing more trials isn’t going to magically bring them closer together)
- More trials MIGHT improve accuracy (if you have only random errors, then more trials will give you an average result closer to the true value, but if you have a systematic error, more trials won’t correct that bias)
A physics students walks halfway to school, realizes she forget her homework, walks back home, then walks from home to school. The distance between her home and school is 0.5 miles. The entire trip took her 15 minutes.
What was her average velocity for the entire trip?
avg vel = 0.5 mi / 15 min = 0.03 mi/min OR 2 mi/hr
avg vel = displacement / time
displacement = final position-initial position = 0.5 mi
Draw a position vs. time, velocity vs. time, and acceleration vs. time graph for an object being dropped off a building, neglecting air resistance.
Acceleration = constant = -9.8 m/s^2
Velocity = linear, starting from v=0, slope=-9.8
Position = quadratic, starting with vertex at max height at time=0, concave down
A baseball is thrown straight up in the air. It reaches a maximum height of 25 m. How long does it spend in the air before it is caught?
t = 4.5 seconds
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v22 = v12 + 2a(x2-x1)
v2 = 0 at top, a = -9.8, x2-x1 = 25 --> v1 = 22.1 m/s
v2 = v1 + at --> t = 2.26 s
total time = 2.26 x 2 = 4.5s
A 5-kg chair sits at rest on the floor. A person tries to pull the chair with a force of 100 N at an angle of 15 deg above horizontal. There is friction between the chair and the floor, with us = 0.4 and uk = 0.15. What is the friction force acting on the chair?
(Use g = 10 m/s2)
Friction Force = 3.6 N
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y-direction: FN + 100sin15 - 50 = 0 --> FN = 24.1N
x-direction: 100cos15 = 97 N
Max static friction = ukFN = 9.65 N
Box Moves, since 97 N > 9.65 N
Friction force = ukFN = 3.62 N
What is the greatest number of significant figures you could include when taking a measurement with a ruler that has tick marks in increments of 10 cm?
2 sig figs
A particle moves on the x-axis. When its acceleration is positive:
A) its velocity must be positive
B) its velocity must be negative
C) it must be slowing down
D) it must be speeding up
E) none of the above must be true
E) none of the above must be true
The diagram shows a velocity-time graph for a car moving in a straight line. At point Q the car must be:
A) moving with zero acceleration
B) traveling downhill
C) traveling below ground-level
D) reducing speed
E) traveling in the reverse direction to that at point P
E) traveling in the reverse direction to that at point P
A soccer ball is kicked at an angle of 30 deg above the horizontal and travels 50 m in 2 seconds. What maximum height did the ball reach?
max height = 0.74 m
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Horizontal: x2-x1 = V1xt --> 50 = V1x(2)
V1x = 25 m/s --> V1cos(30) = 25 --> V1 = 28.9 m/s
Vertical: V1y = 28.9sin(30) = 14.4 m/s
At max height, V2y = 0
Eqn 4: 0 = 14.4 + 2(9.8)(y2-y1) --> y2-y1 = 0.74 m
A 100-kg crate sitting on a 35 degree inclined surface is attached to the wall via a rope. There is no friction between the crate and the surface.
A pulley starts releasing the rope so that the block is slowly allowed to slide down the ramp . What must be the tension in the rope such that the block moves with constant velocity?
T = 574 N
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x-direction: T - 1000cos(55) = ma = 0 (const velocity)
T = 1000cos(55) = 574 N
A student does an experiment with a dynamics cart, where they incrementally increase the mass on the cart and then measure the resulting acceleration when a constant force value is applied. The student then plots their results, with mass as the independent variable and acceleration as the dependent variable.
What will be the mathematical relationship of the resulting equation?
(A) Linear
(B) Inverse
(C) Quadratic
(D) Exponential
(B) Inverse
x = independent = mass
y = dependent = acceleration
F = ma --> a = F/m --> y = const/x --> inverse
An airplane flying at 500 mi/hr flies due east for 30 minutes, then turns and flies due south for 90 minutes. What is the airplane's displacement and direction (angle) from it's starting location?
Disp = 791 mi, Dir = -72 deg OR 288 deg
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East 0.5 hr x 500 mi/hr = 250 mi
South 1.5 hr x 500 mi/hr = 750 mi
Displacement = sqrt(250^2 + (-750)^2) = 791 mi
Direction = tan-1(-750/250) = -72 deg
A car accelerates from rest on a straight road. A short time later, the car decelerates to a stop and then returns to its original position in a similar manner, by speeding up and then slowing to a stop. Which of the following five position vs time graphs best describes the motion?
A bank robber takes a running start off of a building to evade the police. He jumps off the 5 m high building with a horizontal velocity of 3 m/s. At the same time that the bank robber jumps, a getaway car starts driving from the base of the building to catch him. If the car starts at rest, how fast must the car accelerate to reach the man when he would hit the ground?
a = 5.9 m/s2
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(1) Proj Motion -- Vertical motion:
V1y = 0, a = -9.8 m/s2, y2-y1 = -5m
Eqn 3: -5 = 0 + (1/2)(-9.8)t2 --> t = 1.01s
Horizontal Motion: x2-x1 = V1xt = 3.03m
(2) Car's motion:
V1 = 0, x2-x1 = 3.03m, t = 1.01s
Eqn 3: 3.03 = 0 + (1/2)a(1.01)2
a = 5.9 m/s2
A person is standing on a scale in an elevator. When the elevator is at rest, the scale reads 1000 N. As the elevator begins to move downwards, the scale reads 800 N for a duration of 3 seconds, after which the scale returns to reading 1000 N.
What is the top speed reached by the elevator?
top speed = 6 m/s
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Fnet = ma
FN - Fg = ma
800 N - 1000 N = (100 kg)a
a = -2 m/s2
v2 = v1 + at
v2 = 0 + (-2 m/s2)(3 s) = -6 m/s
speed = 6 m/s