Tuesday, October 17, 2017

Pressure (In Solid and In Liquid) Worksheet and Answer For Junior High School

1. Calculate the pressure on a woman’s foot when a woman who weighs 500N steps on her foot with her heels which have total area of 0.5 m2 with all her weight.



2.Calculate the pressure exerted on the floor when an elephant who weighs 6000 N stands on one foot which has an area of 20 m2



3. Calculate the pressure exerted on the heel of a girl’s foot if the girl weighs 500 N and she lands on one heel which has an area of 16 cm2.



4. A woman walking in high heals can damage a hardwood floor by making small dimplesin the floor since her weight is concentrated on such a small area (the tip of thehigh heal). If the woman weighs 500 N and the tip of the high heal is 1/15 m2. what is the pressure exerted on the floor by her high heal?



5. A 75-kg solid cylinder, 2.5 m long and with an end radius of 5.0 cm, stands on one end. How much pressure does it exert?

6.    A barber raises his customer’s chair by applying a force of 150N to a hydraulic piston of area 0.01 m2. If the chair is attached to a piston of area 0.1 m2, how massive a customer can the chair raise? Assume the chair itself has a mass of 5 kg.

7.    A hydraulic system is used to lift a 2000-kg vehicle in an auto garage. If the vehicle sits on a piston of area 0.5 square meter, and a force is applied to a piston of area 0.03 square meters, what is the minimum force that must be applied to lift the vehicle?

8.    A 10 cm3 block of paraffin (a type of wax) weighs 0. 085 N. It is carefully submerged in a container of gasoline. One cm3 of gasoline weighs 0.0069 N.
a. What is the weight of the gasoline displaced by the paraffin?
b. Will the block of paraffin sink or float in the gasoline?

9.     A 70kg ancient statue lies at the bottom of the sea. Its volume is 3 x 104 cm3. How much force is needed to lift it?

10. When a crown of mass 14.7 is submerged in water, an accurate scale reads only 13.4 kg. Is  the crown made of gold? (ρgold = 19,300kg/m3)

Turning effect (Lever, Pulley, and Inclined Plane) Worksheet and Answer For Junior High School

1.First class lever has a 4900N weight located 4 meters from the fulcrum. If the force is applied 8 meters from the fulcrum, how much force is needed?


2.Second class lever has a 19600N weight located 4 meters from the fulcrum.  If the lever is 10 meters long, how much force must be applied at the other end to lift the weight?


3. A third class lever is 4.8 meters long. The fulcrum is at one end. The force is applied 3.0 meters from the fulcrum.  How much force will it take to lift a weight of 160 N?


4. Two boys take a 12 m long board and rest it on a large rock to make a teeter-totter. If the 50 kg boy sits x m from the fulcrum, how far must the 70 kg boy sits from the fulcrum if they balance? (hint: use the 50 kg boy as output/object)


5. The man is lifting a box, it has mass 400 kg, how much force does the man need to apply to lift box?




6. What is the MA of this ramp? Show your work.
a). Calculate the MA
b). Calculate the force do we need to apply to the box




Monday, October 16, 2017

Kinetic Energy and Potential Energy Worksheet and Answer For Junior High School

1. You serve a volleyball with a mass of 2.1 kg. The ball leaves your hand with a speed of 30 m/s. The ball has ______________________ energy. Calculate it.



2. A baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby weighs 12 N. The carriage has ____________ energy. Calculate it.



3. A car is traveling with a velocity of 40 m/s and has a mass of 1120 kg. The car has ___________energy. Calculate it.



4. A cinder block is sitting on a platform 20 m high. It weighs 79 N. The block has _____________ energy. Calculate it.



5. There is a bell at the top of a tower that is 45 m high. The bell weighs 190 N. The bell has ____________ energy. Calculate it.



6. A roller coaster is at the top of a 72 m hill and weighs 966 N. The coaster (at this moment) has ____________ energy. Calculate it.



7. What is the kinetic energy of a 3-kilogram ball that is rolling at 2 meters per second?



8. Object were lifted by a machine. One object had a mass of 2 kilograms if the Kinetic energy of the object was 1600 J. What was the velocity?



9. Determine the kinetic energy of a 1000-kg roller coaster car that is moving with a speed of 20.0 m/s.



Tuesday, April 4, 2017

INFINITE SERIES, POWER SERIES

1. The Geometric Series
     Example of geometric progressions;
a). 2, 4, 8, 16, 32, ...
b) 1, 2/3 , 4/9, 8/27, ...
c) a, ar, ar2, ar3, ...

You may recall that in a geometric progression we multiply each term by some fixed number to get the next term.

The formula for the sum of n terms of the geometric progression is

That geometric series has a sum if and only if |r| < 1, and in this case the sum is
The series is then called convergent.

Problem, Section 1
1. In the bouncing ball example above, find the height of the tenth rebound, and the distance traveled by the ball after it touches the ground the tenth time. Compare this distance with the total distance traveled.(Suppose a bouncing ball rises each time to 2/3 of the height of the previous bounce then it would represent the heights of successive bounces in yards if the ball is originally dropped from a height of 1 yd).
 Answer:
a. The height of the tenth rebound
    1, 2/3 , 4/9, 8/27, ...
    U1 = a = 1 (the originally height)
    U2  = 2/3(the height of the first rebound)
    U3  = 4/9(the height of the second rebound)
      '
      '
    U11  = ? (the height of the eleventh rebound)
    Un= a.rn-1
    U11= 1.(2/3)11-1
    U11= 1.(2/3)10
    U11= 0.017 yd
    So, the height of the tenth rebound is 0.017 yd.

b. The distance traveled by the ball after it touches the ground the tenth time.

c. The total distance traveled.

2. Derive the formula (1.1) for the sum Sn of the geometric progression Sn = a+ar+ar2 + · · · + arn-1. Hint: Multiply Sn by r and subtract the result from Sn; then solve for Sn. Show that the geometric series converges if and only if |r| < 1; also show that if |r| < 1, the sum is given by equation (1.2).

Use equation (1.2) to find the fractions that are equivalent to the following repeating decimals:
3. 0.55555 · · ·  
4. 0.818181 · · ·
5. 0.583333 · · ·
6. 0.61111 · · ·
7. 0.185185 · · ·
8. 0.694444 · · ·
9. 0.857142857142 · · ·
10. 0.576923076923076923 · · ·
11. 0.678571428571428571 · · ·