When we measure physical quantities, the units may be anything that is reasonable as long as they are well defined. It’s usually best to use the international standard units. Density may be defined as the mass of an object divided by its volume. Which of the following units would probably not be acceptable units of density?
A car starts from rest on a circular track with a radius of 150 m. Relative to the starting position, what angle has the car swept out when it has traveled 150 m along the circular track?
Given the following equation: y = c n at 2 , where n is an integer with no units, c is a number between zero and one with no units, the variable t has units of seconds and y is expressed in meters, determine which of the following statements is true.
a) a has units of m/s and n =1.
b) a has units of m/s and n =2.
c) a has units of m/s 2 and n =1.
d) a has units of m/s 2 and n =2.
e) a has units of m/s 2 , but value of n cannot be determined through dimensional analysis.
A displacement vector has a magnitude of 175 m and points at an angle of 50.0 degrees relative to the x axis. Find the x and y components of this vector.
During the execution of a play, a football player carries the ball for a distance of 33 m in the direction 76° north of east. To determine the number of meters gained on the play, find the northward component of the ball’s displacement.
Vector has a horizontal component a x = 15.0 m and makes an angle = 38.0 with respect to the positive x direction. What is the magnitude of a y , the vertical component of vector ?
a) 4.46 m b) 11.7 m
c) 5.02 m d) 7.97 m
e) 14.3 m
42.
Chapter 1: Introduction and Mathematical Concepts Section 8 Addition of Vectors by Means of Components
The drawing above shows two vectors A and B , and the drawing on the right shows their components. Each of the angles θ = 31°.
When the vectors A and B are added, the resultant vector is R , so that R = A + B . What are the values for R x and R y, the x - and y -components of R ?
The displacement vectors A and B , when added together, give the resultant vector R , so that R = A + B . Use the data in the drawing and the fact that φ = 27° to find the magnitude R of the resultant vector and the angle θ that it makes with the + x axis.
Use the component method of vector addition to find the resultant of the following three vectors: = 56 km, east = 11 km, 22° south of east = 88 km, 44° west of south
A) 66 km, 7.1° west of south B) 97 km, 62° south of east
C) 68 km, 86° south of east D) 52 km, 66° south of east
E) 81 km, 14° west of south
47.
Adding Multiple Vectors Adding Vectors F 2 F 3 F 4 F 1
48.
Adding Multiple Vectors F 1 F 2 F 3 F 4 1 2 3 4 F 1 = 50 N 1 = 30 o F 2 = 100 N 2 = 135 o F 3 = 30 N 3 = 250 o F 4 = 40 N 4 = 300 o 43.3 25.0 70.7 70.7 10.3 28.2 20.0 34.6 17.7 32.9
49.
Adding Multiple Vectors F R = 37.4 N R 17.7 32.9
50.
Now You Try: F 1 F 2 F 3 F 4 1 2 3 4 F 1 = 90 N 1 = 45 o F 2 = 80 N 2 = 150 o F 3 = 50 N 3 = 220 o F 4 = 70 N 4 = 340 o
51.
Chapter 1: Introduction and Mathematical Concepts “ Section 9” Additional Stuff You Should Know
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