Physics - Review for 1st Semester Final Key
Experimental Design & Graphical Representation and Interpretation
Given a written description of an experiment you should be able to:
Distinguish between and identify the independent and dependent variables.
The independent variable (IV) is the one you vary or manipulate in the experiment. The dependent (DV)is
the one which is effected by the change.
Correctly place these variables on the appropriate axes when graphing data.
Independent goes on the x-axis, dependent goes on the Y
Example: Two students wanted to determine the relationship between number of cups of coffee consumed
and pulse rate. They had volunteers drink 1, 2, 3, & 4 cups of coffee and recorded their pulse rate 10
minutes after each cup.
a) Identify the independent and dependent variables.
IV = # cups
DV = pulse rate
b) Which variable will go on the x-axis?
IV = # cups
2.
Demonstrate your understanding of the relationships y  x , y 
1
2
2
, y  x , y  x in the following ways
x
a. sketch or recognize the basic graphs of each
b. make basic predictions based on the relationship;
Example: The mass and acceleration of an object are inversely related; if the mass doubles, the acceleration
will _____be half as much___________....
Given a graph which is not linear, manipulate the variables so as to produce a straight-line graph.
Example: For the graph at left describe what you would do to generate a straight line graph
plot X vs T2
X (m)
3.
T (s)
1st semester Review - page 1
4.
Derive an equation of a straight line, given the statistics. Decide whether to keep or discard the y-intercept;
be able to justify your decision.
V2=2.7m2/s2/m H + .0314 m2/s2
Kinematics- U1 Constant Velocity
Kinematics is the study of how things move. In Unit 1 we looked at objects moving at a constant velocity.
Given a X vs T, or V vs T graph of an object moving at a constant velocity you should be able to describe the
motion of the object, including speed, direction, and displacement. You should also be able to produce a
motion map.
Example: Sketch the V vs T graph and motion map for the X vs T graph below
X
V
T
T
0
Example: Determine the speed of the object whose motion is described by the graph at right and write
the equation for the line.
Find slope, should be 4m/6s = ,67 m/s
X
6
5
4
3
2
1
1 2 3 4 5 6
1st semester Review - page 2
T
Example: How far did objects A and B travel in 3 seconds?
Find area under curve, for A = 9m, for B = 9m
Kinematics- U2 Constant Acceleration
In Unit 2 we examined objects experiencing a change in velocity (acceleration). Given a X vs T, or V vs T , or
A vs T graph of an object moving with a changing velocity you should be able to describe the motion of the
object, including speed, direction, and displacement. You should also be able to produce a motion map.Also
use the following equations to solve problems: v  at  v0 , x  12 at 2  v0t , v 2f  v20  2ax
Example: How does the displacement, instantaneous velocity, and acceleration of object A compare to object B
at 3 s?
A
B
X
T
Sketch a motion map for both A and B
A
B
0
Example: Determine the acceleration of the object whose motion is depicted at left. Write the equation for the
line.
6
5
A=∆V/∆T, a=5m/s / 4sec = 1.25m/s2
V 4
3
2
1
1 2 3 4 5 6
T
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Example: Draw the corresponding graphs based upon the information provided in the given graph.
x
x
x
t
t
V
V
V
t
t
t
a
a
a
t
t
t
Examples: A cart travels along a straight section of road. A velocity vs time graph illustrating its motion is
graphed to the right.
(a) Indicate every time t for which the cart is at rest.
A, C, F
(b) Indicate every time interval for which the speed
(magnitude of velocity) of the cart is increasing.
a-b, c-d, f-g
(c) What is the acceleration from a – b?
5m/s /3s = 1.7m/s2
v (m/s)
b
5
g
c
a
5
15
10
5
(d) What is the acceleration from b – c?
-1.7m/s2
(e) What is the acceleration from d – e?
Zero, moving at a const vel
f
d
e
velocity time graph
(f) What is the acceleration from e – g?
3- -5m/s2 / 3s = 2.7m/s2
1st semester Review - page 4
t (s)
SC81
1st Semester Review –pt 2
2-D Motion
In Unit 3, 2D motion, we examined the motion of projectiles. A projectile follows a parabolic path. The
horizontal motion of the projectile is constant velocity, the vertical motion is acceleration. Use the kinematic
equations from Units 1&2 to solve projectile problems.
Example: You are on top of a building that is 55.0 m tall. You toss a ball straight up. It travels 35.0 m up
before it stops and begins to fall back down. (a) What was the ball’s initial velocity? It goes up and then falls
down to the ground below. (b) How much time is it in the air?
a) Vf2 = 2A∆X+ Vi2, at the top of the flight the V is zero so
Vi = 26.5 m/s
0 = 2(-10 m/s2)(35 m) + Vi2,
b) Several methods, Vi = Vf, so use Vf = AT + Vi, -26.5 m/s = (-10 m/s2)T + 26.5 m/s , T= 5.3s
Example
A 5 kg bowling ball rolls off the roof of a 50 m building at 12 m/s.
a. How long does it take the ball to reach the ground?
∆Y = 1/2 AT2 + VyT, Vy =0, so 50m = ½(-10 m/s2)T2, T = 3.16 s
b. How far from the building does it hit?
∆X = VT + X0, ∆X = 12 m/s (3.16s) + 0, ∆X = 37.9 m
2. Repeat problem 1 above with the ball leaving at a 30˚ angle.
Vx = 10.45 m/s
Time 3.82 s, ∆X = 39.5m
Vy = 6.0 m/s
Statics
In Unit 4 we moved from how things moved to why things move . Objects in Unit 4 are moving at a constant
speed, with no net force. You should be able to state and give examples of Newton's 1st and 3 rd laws. You should
also be able to draw a force diagram for an object in static equilibrium and solve any of the forces acting on the
object.
Examples: Draw a force diagram that correctly depicts the forces acting on a given object.
1. A stapler sits motionless on a desk.
2. A ball rolls across the floor at constant speed.
1st semester Review - page 5
3. A box sits motionless on an angled ramp.
4.
The boy pushes the mower at constant speed.
If the boy is pushing the mower (m=75kg) with a 200 N force at an angle of 37˚, calculate the frictional force
necessary to keep the mower moving at a constant velocity.
∑ F = 0, Fs + Fb/x = 0, Fs + 200n cos(37) = 0, Fs = 160 N
Examples: solve static problems
Write the equation which describes the forces which act in the xdirection.
∑ Fx = 0, T2 + T1x = 0, T2 + T1sin(25) = 0
Write the equation which describes the forces which act in the ydirection.
∑ Fy = 0 W + T1cos (25) = 0, T1 = 50N/cos25, T1 = 55.2 N
Determine the magnitude of T1 and T2. T2 + 55.2 N sin(25) = 0, T2 = 23.3 N
Examples: State and give an example, using force diagrams, of Newton's 3rd law.
A horse exerts a 500 N force on a heavy wagon, causing it to accelerate. What force does the wagon exert
on the horse?
The Forces are the same 500N
Part 2
Dynamics
In unit 5 we had objects accelerating due to a net force. You should be able to state and give examples of
Newton's 2nd law. You should also be able to draw a force diagram for an object experiencing a net force
and solve for any of the forces acting on the object or the acceleration.
Examples
a. Sketch the graphs that show the relationship between acceleration and force and between acceleration
and mass.
A
A
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F
M
b. If the same force is applied to two objects, one 10 kg and the other 20 kg, how do their accelerations
compare?
A α 1/m , so if mass is doubled then A would be 1/2
c. Compare the acceleration a hockey puck experiences when first 5 N, then 10 N of force is applied.
A α F, so if F is doubled then A would double also
Draw a force diagram to represent the situation, then write equations for objects experiencing multiple forces,
and solve for acceleration or force.
Examples
1. What is the acceleration of an 800 kg elevator when the cable applies
10 000N force upward?
∑ Fx = ma, Fc + Fe = ma, 10,000 N -8000 N = 800 kg A, A = 2.5 m/s2
2. What is the tension in the cable if the elevator accelerates downward at 3.0 m/s2?
∑ Fx = ma, Fc + Fe = ma, Fc -8000 N = 800 kg -3.0 m/s2 , Fc = 5600 N
3. What would be the apparent weight of a 70 kg boy in the elevator in (2)?
∑ Fx = ma, Fn + Fe = ma, Fn -700 N = 70 kg -3.0 m/s2, Fn = 490 N
a. What is the Fg in the
x-direction?
Fgx = 50sin(15) = 12.9 N
b. What is the acceleration of the box down the ramp?
∑ Fx = ma, Fex = ma, 12.9 N = 5.0 kg A, A= 2.6 m/s2
c. How fast would the block be moving after sliding 2.0m?
Vf2 = 2A∆X+ Vi2, Vf = 10.4 m/s
5. A 5.0 kg box is pulled along a frictionless surface by a 40N force acting at a 30° angle from the horizontal.
∑ Fx = ma, Ftx = ma, 40 Ncos(30) = 5.0 kg A, A = 6.9 m/s2
b. What is the normal force acting on the box?
∑ F = 0, Fn + Fty + Fe = 0, Fn + 40 Nsin(30) – 50N = 0, Fn = 30 N
1st semester Review - page 7
Momentum
We did a brief examination of momentum which is the product of mass and velocity. Momentum is a conserved
quantity, the total momentum in a system remains constant. You should be able to solve problems with both
elastic and inelastic collisions. We also looked at change in momentum and the impulse necessary to cause a
change. You should be able to solve impulse problems.
Example:
1. A bumper car with Stunt Man Nyall as the driver (total mass = 80 kg), moving at 10.0 m/s, collides with a
stationary bumper car with Nyall’s brother Brent as the driver (total mass = 70 kg). After the collision, Nyall’s
car has a velocity of – 2.0 m/s.
a. Draw diagrams representing the bumper cars before and after the collision.
B4
After
Nyall
Brent
Nyall
Brent
b. What is the velocity of Brent’s car after the collision?
mv + mv = mv + mv
80 kg(10 m/s) + 0 = 80 kg(-2.0 m/s) + 70 kg v
V = 13.7 m/s
c. What is the change in momentum of Nyall’s car?
∆ρ = m∆v, ∆ρ = 80 kg (-2.0 – 10m/s), ∆ρ = 960 kgm/s
d. If the cars are in contact for 0.200s, what is the magnitude of the force each car exerts on the other?
F∆T = m∆v, F(0.200s) = 960 kgm/s, F= 4800 Ns
Uniform Circular Motion
In Unit 6 we examined objects in circular motion which were moving at a constant speed, but experiencing a net
inward acceleration due to the constant change in direction. The acceleration toward the center of the circle
results in a net force towards the center. You should be able to convert from radians to degrees and find the
angular velocity and acceleration of spinning objects. You should also be able to solve for any forces acting on the
rotating object.
Example:
3. Izzy Dizzy is doing doughnuts in the mall parking lot. If his car is moving along a circular path of radius 25.0 m
at a speed of 15.0 m/s, what is the centripetal acceleration of Izzy and his car?
A = V2/r
A = (15m/s)2/25m, A= 9.0m/s2
4. At what constant speed would Izzy (mass 80 kg), have to be traveling in order to feel weightless as he drives
over the top of a hill with a radius of curvature of 20 meters?
Be sure to draw a force diagram to represent the situation.
∑ Fx = ma, Fn + Fe = ma, If he feels weightless then the Fn =0, so Fe = ma
-800 N = 80 kg V2/20 m, V = 14.1 m/s
1st semester Review - page 8