# Math Review

```Yuko Hori - PHY 2048C - General Physics
A (S
Math
Problems from the Whole Course
1
Review
Exercise
Due date: Wed Jan 14 11:59:59 pm 2015 (EST)
Volume of a Sphere
Triangle - Law of Cosines
10
Calculate the volume of a spherical balloon which has a surface area of 0.0751 m2
Area and Volume relations
γ
8
7
6
Y (cm)
You are correct. Your receipt no. is 162-6453
9
5
4
Part A
There are two roots for the following equation. (i.e., two
values of y for which Z equals zero.)
Z = 2.5y2 -9.87y + 1.60
Calculate the more positive of the two.
3
b
2
β
α
1
a
c
0
0
1
2
3
4
5
6 7
X (cm)
8
9
10 11 12 13
Part A
You are correct. Your receipt no. is 162-9311 Part B
What is the other root of this equation?
The angle β = 110◦ . What is the length of a?
You are correct. Your receipt no. is 162-150 Part B
What is the length of b?
You are correct. Your receipt no. is 162-5237 Part C
For what value of y does Z achieve its minimum value?
You are correct. Your receipt no. is 162-6006 Part C
What is the angle α?
You are correct. Your receipt no. is 162-4744
You are correct. Your receipt no. is 162-6314
Arc Length
7
6
5
Y
4
s
3
2
θ
1
0
0
1
2
3
4
5
X
6
7
8
9
10
Part A
The figure represents a section of a circle. What is the angle
θ?
You are correct. Your receipt no. is 162-458 Part B
What is the arc length s?
You are correct. Your receipt no. is 162-9774
Yuko Hori - PHY 2048C - General Physics A (S
3 - Vectors and 2D Motion
3
Due date: Mon Jan 26 11:59:59 pm 2015 (EST)
Force Exerted By Fleas
Part A
A flea pulls on a puck with force 10 microN at an angle of
45◦ . Another flea pulls on the puck with force 1 microN at an
angle of 0◦ . (See diagram for angle scale.) Draw vectors on
the diagram to scale representing the forces. Carefully add
the vectors tip-to-tail. (Use a ruler.) What is the magnitude
of the net force on the puck?
120&deg;
105&deg;
90&deg; 75&deg;
60&deg;
135&deg;
45&deg;
150&deg;
30&deg;
165&deg;
15&deg;
180&deg;
0&deg;
–165&deg;
–15&deg;
–30&deg;
–150&deg;
–135&deg;
–120&deg;
–45&deg;
–105&deg; –90&deg; –75&deg;
–60&deg;
You are correct. Your receipt no. is 162-3641 Part B
At what angle is the net force? (Answer in ◦ using the angle
scale provided.)
You are correct. Your receipt no. is 162-7806 Part C
A third flea decides to pull the puck so that it will stop accelerating. What is the magnitude of the force with which it
must pull?
You are correct. Your receipt no. is 162-7642 Part D
In what direction must the third flea pull so that the puck
stops accelerating? (Answer in ◦ using the angle scale provided.)
You are correct. Your receipt no. is 162-3806