The pole in Figure 5.24 is at a 90.0° bend in a power line and is therefore subjected to more shear force than poles in straight parts of the line. The tension in each line is 4.00 × 10 4 N, at the angles shown. The pole is 15.0 m tall, has an 18.0 cm diameter, and can be considered to have half the stiffness of hardwood. (a) Calculate the compression of the pole. (b) Find how much it bends and in what direction. (c) Find the tension in a guy wire used to keep the pole straight if it is attached to the top of the pole at an angle of 30.0° with the vertical. (Clearly, the guy wire must be in the opposite direction of the bend.)
The pole in Figure 5.24 is at a 90.0° bend in a power line and is therefore subjected to more shear force than poles in straight parts of the line. The tension in each line is 4.00 × 10 4 N, at the angles shown. The pole is 15.0 m tall, has an 18.0 cm diameter, and can be considered to have half the stiffness of hardwood. (a) Calculate the compression of the pole. (b) Find how much it bends and in what direction. (c) Find the tension in a guy wire used to keep the pole straight if it is attached to the top of the pole at an angle of 30.0° with the vertical. (Clearly, the guy wire must be in the opposite direction of the bend.)
The pole in Figure 5.24 is at a 90.0° bend in a power line and is therefore subjected to more shear force than poles in straight parts of the line. The tension in each line is
4.00
×
10
4
N, at the angles shown. The pole is 15.0 m tall, has an 18.0 cm diameter, and can be considered to have half the stiffness of hardwood. (a) Calculate the compression of the pole. (b) Find how much it bends and in what direction. (c) Find the tension in a guy wire used to keep the pole straight if it is attached to the top of the pole at an angle of 30.0° with the vertical. (Clearly, the guy wire must be in the opposite direction of the bend.)
5. The radius of a circle is 5.5 cm.
(a) What is the circumference in meters?
(b) What is its area in square meters?
6. Using the generic triangle below, solve the following:
0 = 55 and c = 32 m, solve for a and b.
a = 250 m and b = 180 m, solve for the angle and c.
b=104 cm and c = 65 cm, solve for a and the angle
b
a
7. Consider the figure below representing the Temperature (T in degrees Celsius) as a function of time
t (in seconds)
4
12
20
(a) What is the area under the curve in the figure below?
(b) The area under the graph can be calculated using integrals or derivatives?
(c) During what interval is the derivative of temperature with respect to time equal to zero?
Part 3: Symbolic Algebra
Often problems in science and engineering are done with variables only. Don't let the different letters
confuse you. Manipulate them algebraically as though they were numbers.
1. Solve 3x-7= x + 3 for x
2x-1
2. Solve-
for x
2+2
In questions 3-11 solve for the required symbol/letter
3. v2 +2a(s-80), a =
=
4. B=
Ho I
2π r
5. K = kz²
6.xm=
MAL
,d=
d
7.T, 2
=
8.F=Gm
9. mgh=mv²
10.qV = mu²
80
12. Suppose that the height in meters of a thrown ball after t seconds is given by h =6+4t-t².
Complete the square to find the highest point and the time when this happens.
13. Solve by completing the square c₁t² + cat + 3 = 0.
14. Solve for the time t in the following expression = 0 + vot+at²
A blacksmith cools a 1.60 kg chunk of iron, initially
at a temperature of 650.0° C, by trickling 30.0°C
water over it. All the water boils away, and the iron
ends up at a temperature of 120.0° C.
For related problem-solving tips and strategies, you
may want to view a Video Tutor Solution of
Changes in both temperature and phase.
Part A
How much water did the blacksmith trickle over the iron?
Express your answer with the appropriate units.
HÅ
mwater =
Value
0
?
Units
Submit
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