Page 104 Practice Problem 4.4: If passenger comfort requires that the acceleration should be no greater in magnitude than 0.10g, what distance is required to stop the car if its speed is initially 30m/s (roughly 60mi/h)? What force is required? Answers: 459m, 1960 N.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
![Page 104 Practice Problem 4.4: If passenger comfort requires that the acceleration should be
no greater in magnitude than 0.10g, what distance is required to stop the car if its speed is
initially 30m/s (roughly 60mi/h)? What force is required? Answers: 459m, 1960 N.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28764828-4d1c-44b8-9544-7d79c8b69e6b%2F2cd332f6-e5df-48c8-849e-051572a85c10%2Fm1nlr1_processed.jpeg&w=3840&q=75)
![EXAMPLE 4.4 Quick stop of a heavy car
In this example we consider a problem in which the weight of an object is given directly, but not its mass.
To use Newton's second law, we will, of course, first have to determine the object's mass. A big luxury car
weighing 1.96 X 104 N (about 4400 lb), traveling in the +x direction, makes a fast stop; the x component
of the net force acting on it is -1.50 X 104 N. What is its acceleration?
OXO
SOLUTION
SET UP Figure 4.19 shows our diagram. We draw the weight as a force
with magnitude w. Because the car does not accelerate in the y direc-
tion, the road exerts an upward normal force of equal magnitude on the
car; for completeness, we include that force in our diagram.
SOLVE To find the acceleration, we'll use Newton's second law,
EF= max. First, however, we need to find the car's mass. Since
we know the car's weight, we can find its mass m from Equation 4.9,
w = mg. We obtain
m =
Mary
Then, EF, = ma, gives
ax=
W
DAD
8
Fx
1.96 × 104 N
9.80 m/s²
m
-1.50 × 104 N
2000 kg
=
= -7.5 m/s².
Video Tutor Demo
.
1.96 x 104 kg m/s²
9.80 m/s²
= 2000 kg.20.
-1.50 × 104 kg m/s²
2000 kg
ā
F = -1.50 x 104 N
Video Tutor Solution
n = 1.96 x 104 N
eno morì 2917 155 do 10 1
A FIGURE 4.19 Our diagram for this problem.
W 1.96 x 10+ N
REFLECT This acceleration can be written as -0.77g. Note that
-0.77 is also the ratio of -1.50 X 104 N to 1.96 x 104 N. An accel-
eration of this magnitude is possible only on a dry paved road. Don't
expect it on a wet or icy road!
Practice Problem: If passenger comfort requires that the acceleration
should be no greater in magnitude than 0.10 g, what distance is required
to stop the car if its speed is initially 30 m/s (roughly 60 mi/h)? What
force is required? Answers: 459 m, 1960 N.
Usually, the easiest way to measure the mass of an object is to measure its weight, often
by comparison with a standard weight. In accordance with Equation 4.10, two objects that
have the same weight at a particular location also have the same mass. We can compare
weights very precisely: The familia](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28764828-4d1c-44b8-9544-7d79c8b69e6b%2F2cd332f6-e5df-48c8-849e-051572a85c10%2Flk6i6rp_processed.jpeg&w=3840&q=75)
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