Variation Problems - Please Solve These For Me. I Need To Pass An Exam!, Exercise 16, 1.\Tthe Force (F) Exerted By An Object Varies Directly As Its Ma

VARIATION PROBLEMS - Please solve these for me. I need to pass an Exam!

EXERCISE 16
1. The force (F) exerted by an object varies directly as its mass (m). If the force is 20 dynes when the mass is 440 kg., find the force when the mass is 1100 kg.

2. Hooke's Law states that the distance (d) that a spring is stretched varies directly as
the weight (w) on the end of the spring. If the distance is 48 cm. when the weight is 120 gms., find the weight when the distance is 72 cm.

3. The amount of garbage varies directly as the number of people. If town A (population 50,000) produces 24 tons of garbage in a certain period, how much garbage would town B (population 2 million) produce in the same time period.

4. The amount of paper that is recycled varies directly as the acres of land which are saved from logging. If 5 tons of paper is recycled, 120 acres of trees are saved. How many tons of recycled paper are needed to save 300 acres of trees?

5. Time varies inversely as speed. If it takes 3 hrs. to paddle a certain distance at 5 km. per hour, how long would it take to paddle the same distance at 2 km. per hr.?
6. The time to complete a job varies inversely as the number of people who are working.
If it takes 7 people 11 days to complete a job, how long would it take 3 people to complete the same job?

7. The current (I) in an electric circuit varies inversely as the resistance (R).
If the current is 0.3 amperes when the resistance is 45 ohms, find the resistance when the current is 1.6 amperes.

8. Time varies inversely as speed. If the speed is 20 km./hr. for a time of 3 hrs., what would be the speed if the time is 30 minutes?


 
FORMULAE AND MIXED VARIATION
EXERCISE 10
1. Force (F) varies directly as the square of the velocity (v) and inversely as the distance (r).
a) Find the formula for Force.
b) Find the constant k, if F = 24, v = 6, r = 18.
c) Find the velocity if F = 6 and r = 50.
2. The volume (V) of a cylinder varies directly as the product of the radius (r) squared, and the height (h).
a) Find the formula for volume of a cylinder.
b) Find the constant k if v = 314, h = 4, and r = 5.
c) Find the height (h), if v = 4,000,000 and r = .00001.
3. y varies directly as x2 and inversely as z.
a) Find the formula for y.
b) Find the constant k, if x = 0.2, z = 1.06, and y = 20
c) Find z if y = 20,000 and x = .002.
4. The force (F) between two objects varies directly as the product of the masses (m1 and m2) of the objects, and inversely as the square of the distance (r) between them.
a) Find the formula for force (F).
b) Find k, if F = .00005, m1 = 20,000,000, m2 = 100,000, and r = 2000.
c) Find m1, if F = .002, m2 = 30,000, and r = 10,000.

 

VARIATION PROBLEMS

EXERCISE 16.

1. F = 50 dyne

2. W = 180 gms

3. 960 tons of garbages

4. 12.5 tons of recycled papers

5. 7.5 hr

6. 25 2/3 days

7. 8.4375 R

8. 2/3 km/hr

FORMULAE AND MIXED VARIATION

EXERCISE 10.

1. a. F = ((v^2)(k))/r

b. k = 12

c. v = 10√3

2. a. V = (r^2)(h)(k)

b. k = 3.14

c. h = 4.00 x 10^6

3. a. y = ((x^2)(k))/z

b. k = 530

c. z = 1.00 x 10^-7

4. a. F = ((m1)(m2)(k))/r^2

b. k = 1.00 x 10^-10

c. m1 = 6 2/3

(NOTE: Since k is included and is a constant, I included it there; although, it is really unnecessary. I think...)