4. (a) Assume the equation x = At + Bt describes the motion of a particular object, with x having the dimen- sion of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt= 3At + B.3 7. FAT T.B
4. (a) Assume the equation x = At + Bt describes the motion of a particular object, with x having the dimen- sion of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt= 3At + B.3 7. FAT T.B
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Could you solve 14th question please?
![16
Chapter 1 Physics and Measurement
30.231
(a) Determine the proper units for momentum using
dimensional analysis. (b) The unit of force is the new-61o24
ton N, where 1 N 1 kg m/s. What are the units.of
momentumpin terms of a newton and anothher funda-
piental SI uit?
12 Newton's law of universal gravitation is represented by
GMm
30.131
MM.X
where F is the magnitude of the gravitartional force
exerted by one small object on another, M and m are
the masses of the objects, and ris a distance. Force has
the SI units kg m/s. What are the SI units of the pro- W (a
portionality constant G? G2
13. The position of a particle moving under uniform accel-
eration is some function of time and the acceleration.
22. A
ta
Suppose we write this position as x = ka e, where k is a
dimensionless constant. Show by dimensional analysis
that this expression is satisfied if m 1 and n 2. Can
this analysis give the value of k? =
14. (a) Assume the equation x =At + Bt describes the
motion of a particular object, with x having the dimen-
sion of length and t having the dimension of time.
Determine the dimensions of the constants A and B.
23.
24.
M
(b) Determine the dimensions of the derivative dx/dt =
25.
トミドー
Section 1.4 Conversion of Units
3A + B.L tT L AT
T.B
FAT!
to
15. A solid piece of lead has a mass of 23.94 g and a volume
W of 2.10 cm3. From these data, calculate the density of
26
lead in SI units (kilograms per cubic meter). 23.9L10
23.95
6. An ore loader moves 1 200 tons/h from a mine to the
surface, Convert this rate to pounds per second, using
20
1 ton 2 000 lb.
1200 fors
62-
36బది్వ
7. A rectangular building lot has a width of 75.0 ft and
a length of 125 ft. Determine the area of this lot in
square meters. 3.281f=1m
8. Suppose your hair grows at the rate 1/32 in. per day.
V Find the rate at which it grows in nanometers per sec-
ond. Because the distance between atoms in a mole-
cule is on the order of 0.1 nm, your answer suggests
how rapidly layers of atoms are assembled in this pro-
tein synthesis.
75.0x125k 1m
3-2g*
24
32 T
146)
9. Why is the following situation impossible? A student's dor-
mitory room measures 3.8 m by 3.6 m, and its ceiling
is 2.5 m high. After the student completes his physics
course, he displays his dedication by completely wall-
papering the walls of the room with the pages from his
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9346b20-2e1d-49c9-976d-826d91113554%2F59a2e21c-8c76-4100-b315-3b202ca6a398%2Fbe69779_processed.jpeg&w=3840&q=75)
Transcribed Image Text:16
Chapter 1 Physics and Measurement
30.231
(a) Determine the proper units for momentum using
dimensional analysis. (b) The unit of force is the new-61o24
ton N, where 1 N 1 kg m/s. What are the units.of
momentumpin terms of a newton and anothher funda-
piental SI uit?
12 Newton's law of universal gravitation is represented by
GMm
30.131
MM.X
where F is the magnitude of the gravitartional force
exerted by one small object on another, M and m are
the masses of the objects, and ris a distance. Force has
the SI units kg m/s. What are the SI units of the pro- W (a
portionality constant G? G2
13. The position of a particle moving under uniform accel-
eration is some function of time and the acceleration.
22. A
ta
Suppose we write this position as x = ka e, where k is a
dimensionless constant. Show by dimensional analysis
that this expression is satisfied if m 1 and n 2. Can
this analysis give the value of k? =
14. (a) Assume the equation x =At + Bt describes the
motion of a particular object, with x having the dimen-
sion of length and t having the dimension of time.
Determine the dimensions of the constants A and B.
23.
24.
M
(b) Determine the dimensions of the derivative dx/dt =
25.
トミドー
Section 1.4 Conversion of Units
3A + B.L tT L AT
T.B
FAT!
to
15. A solid piece of lead has a mass of 23.94 g and a volume
W of 2.10 cm3. From these data, calculate the density of
26
lead in SI units (kilograms per cubic meter). 23.9L10
23.95
6. An ore loader moves 1 200 tons/h from a mine to the
surface, Convert this rate to pounds per second, using
20
1 ton 2 000 lb.
1200 fors
62-
36బది్వ
7. A rectangular building lot has a width of 75.0 ft and
a length of 125 ft. Determine the area of this lot in
square meters. 3.281f=1m
8. Suppose your hair grows at the rate 1/32 in. per day.
V Find the rate at which it grows in nanometers per sec-
ond. Because the distance between atoms in a mole-
cule is on the order of 0.1 nm, your answer suggests
how rapidly layers of atoms are assembled in this pro-
tein synthesis.
75.0x125k 1m
3-2g*
24
32 T
146)
9. Why is the following situation impossible? A student's dor-
mitory room measures 3.8 m by 3.6 m, and its ceiling
is 2.5 m high. After the student completes his physics
course, he displays his dedication by completely wall-
papering the walls of the room with the pages from his
2.
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