Circular Motion
Uniform circular motion occurs when an
object moves in a circular path with a constant
speed.
The change in velocity, v = vf - vi, is related to the
acceleration.
aavg = =
t
The acceleration is always perpendicular to the path of
the mo
Tutorial One, Two and Three Dimensional Motion
Example:
A car travelling at a constant speed of 45 m/s passes a policeman hidden behind a
building. One second (1.00 s) later the policeman sets out to catch the car,
accelerating at a constant rate of 3.00
Friction:
Example: A crate of mass m is resting on the
bed of a dump truck. In order to make the
crate slide, the track accelerates to the
right. Determine the smallest acceleration
for which the crate will begin to slide.
The crate and the truck have t
Example 1(solved in tutorial):
On a compact disc (CD), audio information is stored
in a series of pits and flat areas on the surface
(binary zeros and ones). The tangential speed of the
CD surface at any location (near the center of the
outer edge) must b
Example: An electric motor turns a flywheel through a drive
belt. The flywheel is a disk of mass M = 80.0 kg and radius R =
0.625 m. The small pulley attached to the flywheel has
negligible mass and radius r = 0.230 m. When the tension in the
upper (taut)
Example: An engine pulls a 1000.0 kg crate from rest to 20.0
m/s in 5.00 s with constant acceleration. The force of kinetic
friction between the crate and the ground is fk = 500.0 N. How
much work is done by the engine?
Wnet = K = mvf2 0
Wengine + Wfricti
Two blocks with masses m] = 2.0 kg and 1n; = 3.0 kg hang on either side ofa pulley, as shown
below. Block m. is in an incline (6 z 300) and is attached to a spring whose constant k = 20.0
N/m. The coefficient of kinetic friction between mass m; and the in
Example. Determine the moment of the force F about
point C.
MC = rCA F =
rCA = -2.0i (m)
2.004.00+3.00
F =F F = (500.0 N)
= (500.0 N)
2+
2
4
557
2
MC = rCA F = 2.00
186
MC =
2+
3
2
=
= 186i -371j + 279k
0
371
+ 743
0 = 557j + 743k
279
2
= 929 N m
Example
Example: Using the method of joints, determine the force in each member of the truss.
Example: Using the method of joints, determine the force in each member of the truss.
Example: Use the method of sections to determine forces in members BC, BG and FG.
E
Example: A plane is flying horizontally at an altitude of 4.20 km.
When the plane is directly overhead, a projectile is fired at an
angle = 54.70 with the ground and has an initial speed of 389
m/s. The projectile hits the plane. Determine the speed of th
’ Two skaters A and B move perpendicular to each other (along x and y axes; respectively) and
collide. After the collision, which takes only 0.15 s, they stick together and move as one unit. The
skater A has mass MA = 75 kg and moves at 10 m/s and the ska
Exercise: Express forces F1, F2 and F3 in
terms of unit vectors and then determine
the resultant force.
F1 = (50) i + (50) j = 30i + 40j (N)
3
5
4
5
F2 = (10cos 600) i +(10 sin 600) j = 5.0i + 8.7j (N)
F3 = -60 j (N)
= tan = 240
-1 11
Resultant force FR
Error Calculations
Example:
The following quantities were measured:
L = (2.47 0.04) m
(3 SF)
P = (0.741 0.002) m
(3 SF)
R = (5.4 0.1) m
(2 SF)
Compute Z = L 2P +R and write the result in the form: (Z Z) units
Z = 2 + 2
0.1077 0.1
2
Z = 2.47 2(0.741) + 5.
Forces and Motion
Contact forces: for example, push and pull
forces.
Action-at-a distance forces (so called field
forces); electromagnetic force, gravitational
force and nuclear forces.
Forces are mediated by exchange particles called
gauge bosons. Elec
period (time for one revo
uniform, solid spheres.
Radius ofthe sun Rs : 6.96x10 m.
Radius of the Earth RE - 6.375(106 m.
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Example: A mass (m = 2.0 kg) attached to a spring oscillates according to the
following equation:
x = 0.50 cos(3.0t + 1T-) .
3
where x is in meters and t is in seconds.
a. What is the spring constant?
k
(.0:
m
k = m 032 =(2.0)(3.0)2 ; 18 N/m
b. What
Lab 6 Static Equilibrium
INTRODUCTION
1. Objectives
Students will measure
forces and torques on a platform mounted on an axle; and
forces and torques acting on a model crane.
2. Apparatus
Computer and software data acquisition system, force sensors, mod
Lab 4 Collisions
INTRODUCTION
1. Objectives
Students will
measure forces and accelerations during collisions;
investigate the relationship between the time of collision and magnitude of force; and
measure change of momentum and impulse during collision
Lab 5 Rotational Motion and Moment of Inertia
INTRODUCTION
1. Objectives
Students will
determine the relationship between the centripetal force and angular velocity;
measure the moment of inertia of a disk; and
study the relation between the angular a
Lab 3 Frictional Forces
Objectives
Students will
measure static and kinetic coefficients of friction using different methods and
enhance their knowledge of error analysis.
Apparatus
Computer and software data acquisition system, frictionless track and c
Experiment 1 Errors
INTRODUCTION
1. Objectives
Students will learn to
estimate absolute errors when making measurements using instruments such as ruler,
electronic vernier caliper, micrometer and balance;
evaluate errors for calculated quantities;
stat
Lab 2 Motion in a Straight Line and Newtons Laws
INTRODUCTION
1. Objectives
Students will
learn how to use computer hardware and software acquisition system;
analyze graphs of position and velocity as a function of time for a straight-line motion;
stud
Example: A mass (m = 2.0 kg) attached to a spring oscillates according to the
following equation:
3
x = 0.50 cos(3.0t + )
where x is in meters and t is in seconds.
a. What is the spring constant?
=
k = m 2 =(2.0)(3.0)2 = 18 N/m
b. What is the maximum spee