35. Figure P4.35 represents the total acceleration of a particle moving clockwise in a circle of radius 2.50 m at a
certain instant of time. At this instant, find (a) the radial
acceleration, (b) the speed of the particle, and (c) its tangential accelerat
ight (his hang time), (b) his horizontal and (c) vertical velocity components at the instant of takeoff, and (d) his takeoff angle. (e) For comparison, determine the hang time of a
whitetail deer making a jump with center-of-mass elevations
yi 1.20 m, yma
Section 4.2 Two-Dimensional Motion with
Constant Acceleration
5. At t 0, a particle moving in the xy plane with constant acceleration has a velocity of vi (3.00 2.00 m/s and is
i
j)
at the origin. At t 3.00 s, the particles velocity is
v (9.00 7.00 m/s. F
2.00 m away, at an angle of 30.0o above the horizontal.
With what velocity must the water stream be launched if it
is not to drop more than 3.00 cm vertically on its path to
the target?
19.
A place-kicker must kick a football from a point
36.0 m (about 40
14. A projectile is red at an angle of 30 from the horizontal
with some initial speed. Firing the projectile at what other
angle results in the same horizontal range if the initial
speed is the same in both cases? Neglect air resistance.
15. The maximum r
The terms in the equation must be manipulated as vector
quantities; the vectors are shown in Figure 4.24. The quantity vbr is due north, vrE is due east, and the vector sum of
the two, vbE, is at an angle , as dened in Figure 4.24. Thus,
we can nd the spe
(2) free-fall motion in the vertical direction subject to a constant downward acceleration of magnitude g 9.80 m/s2.
A particle moving in a circle of radius r with constant speed v is in uniform circular motion. It undergoes a radial acceleration ar becau
Path seen
by observer A
Path seen
by observer B
A
A
B
(a)
(b)
Figure 4.22 (a) Observer A on a moving skateboard throws a ball upward and sees it
rise and fall in a straight-line path. (b) Stationary observer B sees a parabolic path for
the same ball.
then
We dene the time t 0 as that instant at which the origins of the two reference
frames coincide in space. Thus, at time t, the origins of the reference frames will be separated by a distance v0t. We label the position of the particle relative to the S fram
at = 0.300 m/s2
at
at
v
v = 6.00 m/s
ar
a
(a)
(b)
Figure 4.20 (Example 4.9) (a) A car passes over a rise that is shaped like a circle.
(b) The total acceleration vector a is the sum of the tangential and radial acceleration
vectors at and ar .
while the t
y
a = ar + at
at
r
a
r
ar
x
O
O
(a)
(b)
Figure 4.19 (a) Descriptions of the unit vectors r and . (b) The total acceleration a of
a particle moving along a curved path (which at any instant is part of a circle of radius r)
is the sum of radial and tangenti
4.5 Tangential and Radial Acceleration
Let us consider the motion of a particle along a smooth curved path where the velocity
changes both in direction and in magnitude, as described in Figure 4.18. In this situation, the velocity vector is always tangent
25.0 m/s
(0, 0)
= 35.0
y
d
x
Figure 4.16 (Example 4.7) A ski jumper leaves the track moving in a horizontal direction.
this order of magnitude. It might be useful to calculate the
time interval that the jumper is in the air and compare it to
our estimate
where v vi vf and r ri rf . This equation can be solved for v and the expression so obtained can be substituted into a v/t to give the magnitude of the average acceleration over the time interval for the particle to move from to :
a
v
v r
t
r t
Now im
r
vi
r
vf
vi
v
ri
O
rf
(a)
(b)
vf
v
(c)
Figure 4.17 (a) A car moving along a circular path at constant speed experiences uniform circular motion. (b) As a particle moves from to , its velocity vector changes
from vi to vf . (c) The construction for deter
speed, a change in direction, or bothall three controls
are accelerators. The gas pedal causes the car to speed
up; the brake pedal causes the car to slow down. The
steering wheel changes the direction of the velocity
vector.
4.3 (a). You should simply th
tion of the total acceleration for these two positions.
(c) Calculate the magnitude and direction of the total
acceleration.
54. A basketball player who is 2.00 m tall is standing on the
oor 10.0 m from the basket, as in Figure P4.54. If he
shoots the bal
45 nose low
r
24 000
Zero-g
1.8 g
1.8 g
0
65
Maneuver time, s
Courtesy of NASA
Altitude, ft
45 nose high
31000
Figure P4.47
48. As some molten metal splashes, one droplet ies off to the
east with initial velocity vi at angle i above the horizontal,
and an
Objects in Equilibrium
T = T
If the acceleration of an object that can be modeled as a particle is zero, the particle is
in equilibrium. Consider a lamp suspended from a light chain fastened to the ceiling,
as in Figure 5.7a. The free-body diagram for the
L
PITFALL PREVENTION
5.8 Free-body Diagrams
The most important step in solving
a problem using Newtons laws is
to draw a proper sketchthe
free-body diagram. Be sure to
draw only those forces that act on
the object that you are isolating.
Be sure to draw a
n = Ftm
n = Ftm
Fg = FEm
Fg = FEm
Fmt
FmE
(a)
(b)
Figure 5.6 (a) When a computer monitor is at rest on a table, the forces acting on the
monitor are the normal force n and the gravitational force Fg . The reaction to n is the
force Fmt exerted by the moni
Conceptual Example 5.2 How Much Do You Weigh in an Elevator?
Solution No, your weight is unchanged. To provide the acceleration upward, the oor or scale must exert on your feet
an upward force that is greater in magnitude than your
weight. It is this grea
5.5 The Gravitational Force and Weight
L
We are well aware that all objects are attracted to the Earth. The attractive force exerted by the Earth on an object is called the gravitational force Fg . This force is directed toward the center of the Earth,3 a
Table 5.1
Units of Mass, Acceleration, and Forcea
System of Units
SI
U.S. customary
a
Mass
Acceleration
Force
kg
slug
m/s2
N kg m/s2
lb slug ft/s2
ft/s2
1 N 0.225 lb.
In the U.S. customary system, the unit of force is the pound, which is dened as
the forc
0
2
4
3
0
1
2
3
4
1
0
1
2
3
4
0
1
2
3
4
F2
F1
F1
Isaac Newton,
English physicist and
mathematician
(16421727)
Isaac Newton was one of the
most brilliant scientists in history.
Before the age of 30, he
formulated the basic concepts
and laws of mechanics,
d
and so on. According to this observation, we conclude that the magnitude of the
acceleration of an object is inversely proportional to its mass.
These observations are summarized in Newtons second law:
When viewed from an inertial reference frame, the acc
5.3 Mass
Denition of mass
Imagine playing catch with either a basketball or a bowling ball. Which ball is more
likely to keep moving when you try to catch it? Which ball has the greater tendency to
remain motionless when you try to throw it? The bowling b
Contact forces
Field forces
m
(a)
M
(d)
q
(b)
+Q
(e)
Iron
(c)
N
S
(f)
Figure 5.1 Some examples of applied forces. In each case a force is exerted on the object within the boxed area. Some agent in the environment external to the boxed area
exerts a force