PHYS 1303
HOMEWORK 10
1.
A race car travels 40 m/s around a banked (45 with the horizontal) circular
(radius = 0.20 km) track. What is the magnitude of the net resultant force on the
80-kg driver of this car?
2.
A 2.5-kg mass attached to the end of a stri
PHYS 1303
HOMEWORK 5
1. At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y
direction and moves in the xy plane with a constant acceleration of
(2. i 4. j m/s 2 . At the instant the x coordinate of the particle is 15 m, wha
PHYS 1303
HOMEWORK 7
1. At an instant when a 4.0-kg object has an acceleration equal to (5i + 3j) m/s2,
one of the two forces acting on the object is known to be (12i + 22j) N.
Determine the magnitude of the other force acting on the object.
2. A person w
PHYS 1303
HOMEWORK 16
1.
Two vectors lying in the xz plane are given by the equations A = 2i + 3k and
B = i + 2k. What is the value of A B ?
2.
A car of mass 1000 kg moves with a speed of 50 m/s on a circular track of radius
100 m. What is the magnitude o
PHYS 1303
HOMEWORK 17
1.
A2.00kgparticlehasavelocity(2.00i3.00j)m/sanda3.00kgparticlehas
velocity(1.00i+6.00j)m/s.Ifbothparticlesstartfromtheorigin,findtheposition
ofthecentreofmassattimetlater. [Hint: Find the position vector of each particle at
time t.
PHYS 1303
HOMEWORK 18
1.
Three 5.0-kg masses are located at points in the xy plane, as shown. What is the
magnitude of the resultant gravitational
y
force (caused by the other two masses) on
the mass at x = 0.40 m, y = 0?
[Hint: Calculate the vector force
PHYS 1303
HOMEWORK 22
1.
Two harmonic (sinusoidal) waves are described by
700
4
3
y1 = ( m )sin x
t
s
m
700
4
y2 = ( m )sin x
t 2
3
m
s
What is the amplitude of the resultant wave y1 + y2?
[Hint: Use a trigonometric identity to write the sum as a produ
PHYS 1303
HOMEWORK 15
1.
A wheel rotating about a fixed axis at a constant angular acceleration of 1.2
rad/s2 has an initial angular velocity of 5.0 rad/s. How long will it take to
undergo 10 complete revolutions?[Hint: Find the total angle turned through
PHYS 1303
HOMEWORK 13
1.
A 0.30-kg object , tied to the end of a 3.0-m string, is released from rest when the
string makes an angle of 50 with the vertical and swings as a pendulum. When
its speed first reaches 3.9 m/s, determine
(a) the objects kinetic e
PHYS 1303
HOMEWORK 3
1. A particle confined to motion along the x axis moves with constant acceleration
from x = 2.0 m to x = 8.0 m during a 2.5-s time interval. The velocity of the
particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this ti
PHYS 1303
HOMEWORK 2
1. The position of a particle moving along the x axis is given by
x = 21+ 22 6. t2 m , where t is in s. [Hint: take care with precision]
t0
(
)
(a) What is the average velocity during the time interval t = 2.0 s to t= 3. s?
0
(b) What
PHYS 1303
HOMEWORK 11
1.
A 5.0-kg object is pulled along a horizontal surface at a constant speed by a 15-N
force acting 20 above the horizontal. How much work is done by this force as
the object moves 6.0 m?
2.
A constant force of 15 N in the negative y
PHYS 1303 Introductory Mechanics
EXEMPLARY SOLUTION
Question
You are driving into St. Louis and in the distance you see the famous Gateway-to-theWest arch. From your guide book you know that this monument rises to a height of 192m.
You estimate your line
PHYS 1303
HOMEWORK 19
1.
A body of mass 5.0 kg is suspended by a spring of constant 490 N/m which
stretches 10 cm when the mass is attached. It is then displaced downward an
additional 5.0 cm and released. What is its position as a function of time y(t)?
PHYS 1303
HOMEWORK 12
1.
The force an ideal spring exerts on an object is given by Fx = kx, where x
measures the displacement of the object from its equilibrium (x = 0) position. If
k = 60 N/m, how much work is done by this force as the object moves from
PHYS 1303
HOMEWORK 8
1.
In the figure, draw and label the force vectors acting through the point where the
3 strings meet. If the tension in string 1 is 34 N and the tension in string 2 is 24 N,
what is the mass of the object shown?
1
2
40
40
M
If = 40 an
HOMEWORK 4
PHYS 1303
Always use a notation (underline, arrow, etc.) to distinguish vectors from scalars.
iandjarevectors.Componentsarescalars.VectorAisnotthesameasitsmagnitudeA.
1. The vectors A, B, and C are shown below.
y
6
4
A
2
x
B
2 C 2
4
6
Draw (to
PHYS 1303
HOMEWORK 1
1.
Using 1 in = 2.54 cm and 1 mile = 5280 feet, find the conversion factor to convert
mi
m
miles per hour
to meters per second to an appropriate precision.
h
s
2.
How many significant figures are in the following quantities?
(a)
PHYS 1303
HOMEWORK 9
1.
Derive the relationship between the coefficient of kinetic friction k and the
angle of application of the least force needed to drag a box at constant speed
across a surface. [Hint: Find a general expression for the force needed as
PHYS 1303
HOMEWORK 21
1.
The variation in the pressure of helium gas, measured from its equilibrium value,
is given by P = 2.90 105 cos (6.20x 3000t) where x and t have units m and s.
Determine the speed, wavelength, and frequency of the pressure wave.
2.
PHYS 1303
HOMEWORK 14
1.
A 2000-kg truck traveling at a speed of 6.0 m/s makes a 90 turn in a time of 4.0 s
and emerges from this turn with a speed of 4.0 m/s. What is the magnitude of
the average resultant force on the truck during this turn?[Hint: Calcu
PHYS 1303
HOMEWORK 20
1.
An earthquake emits both S-waves and P-waves which travel at different speeds
through the Earth. A P-wave travels at 9000 m/s and an S-wave travels at
5000 m/s. If P-waves are received at a seismic station 1.00 minute before an
S-
PHYS 1303
HOMEWORK 6
1. A race car moving with a constant speed of 60 m/s completes one lap around a
circular track in 50 s. What is the magnitude of the acceleration of the race car?
2.
A car travels counterclockwise around a flat circle of radius 0.25 k