Home Page Textbooks Physics: Principles and Problems Page 125: Section Review

Physics: Principles and Problems

9th Edition

Elliott, Haase, Harper, Herzog, Margaret Zorn, Nelson, Schuler, Zitzewitz

ISBN: 9780078458132

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Page 125: Section Review

Exercise 11

Step 1

1 of 2

Distance and displacement do not have to be equal and most often are not. The only case when they are equal is when we go straight from the starting point.
When for example we go from home to school and back the total distance is double the distance from home to school but the displacement in that case is zero because we are back to the starting point.

Result

2 of 2

No.

Exercise 12

Step 1

1 of 2

Subtracting a vector is actually adding to the vector of the opposite direction, ie if we subtract the vector $mathbf{K}$ from the vector $mathbf{ L}$, we actually add the vectors $mathbf{ L} + (- mathbf{ K})$.

$$
begin{align*}
mathbf{K}&=-4 \
mathbf{L}&=6 \
mathbf{L-K}&=? \
\
mathbf{L-K}&=mathbf{L}+mathbf{-K} \
&=6+-(-4) \
&=10
end{align*}
$$

Exercise scan

Result

2 of 2

$$
mathbf{L-K}=10
$$

Exercise 13

Step 1

1 of 3

In this problem we will calculate the vector components for a given vector and angle.

The figure shows a graphical representation of the component form. Exercise scan

Step 2

2 of 3

Known:

$$
begin{align*}
mathbf{M}&=5 \
theta &= 37text{textdegree} \
end{align*}
$$

Unknown:

$$
begin{align*}
mathbf{M_x}&=? \
mathbf{M_y}&=? \
\
mathbf{M_x}&=mathbf{M}cdot cos(theta) \
&=5cdot cos(37text{textdegree}) \
&=boxed{3.993 } \
\
mathbf{M_y}&=mathbf{M}cdot sin(theta) \
&=5cdot sin(37text{textdegree}) \
&=boxed{3.009 }
end{align*}
$$

Result

3 of 3

$$
begin{align*}
mathbf{M_x}&=3.993 \
mathbf{M_y}&=3.009
end{align*}
$$

Exercise 14

Solution 1

Solution 2

Step 1

1 of 2

We will show the result vector in components, and we will calculate it that way.

$$
begin{align*}
mathbf{K}&=-4hat{x} \
mathbf{L}&=6hat{x} \
mathbf{M}&=3.993hat{x}+3.009hat{y} \
mathbf{R}&=? \
\
mathbf{R_x}&=mathbf{K}+mathbf{L}+mathbf{M}hat{x} \
&=-4+6+3.993 \
&=5.993hat{x} \
\
mathbf{R_y}&=mathbf{M}hat{y} \
&=3.009hat{y} \
\
R&=sqrt{mathbf{R^2_x}+mathbf{R^2_y}} \
&=sqrt{5.993^2+3.009^2} \
&=6.706
end{align*}
$$

Result

2 of 2

$mathbf{R}=5.993hat{x}+3.009hat{y}$

$$
R=6.706
$$

Step 1

1 of 2

In the x direction:

$R_x = M_x + L_x – K_x = 4.0 + 6.0 – 4.0 = 6.0$

In the y direction:

$R_y = M_y + L_y + K_y = 3.0 + 0.0 + 0.0 = 3.0$

Thus the sum of the vectors is:

$$
R = sqrt{R_x^2 + R_y^2} = sqrt{(6.0)^2 + (3.0)^2} = 6.7
$$

Result

2 of 2

6.7

Exercise 15

Step 1

1 of 2

In ordinary arithmetic and algebra, the commutative operations are multiplication and addition. The non-commutative operations are subtraction, division, and exponentiation.

Result

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In ordinary arithmetic and algebra, the commutative operations are multiplication and addition. The non-commutative operations are subtraction, division, and exponentiation.

Exercise 16

Step 1

1 of 2

In this problem, we will consider vector addition. The figure shows the vector summation of two and three different vectors.

When adding two vectors, we get the smallest sum when they are in the same direction and opposite orientation, but because they are of different magnitudes, that sum will never be zero.

When adding three vectors it is possible to get the sum of zeros, they just have to form a triangle. Exercise scan

Result

2 of 2

Two vectors of unequal amount cannot be summed to zero but three can.

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Page 125: Section Review

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