Potential Energy and Kinetic Energy... HELP!?

Question

A man pushes a cart up a ramp thats is 4 meters high and 16 meters long. The cart weights 250 Newtons. How much work was done?


How much effort did the man have to use to push the cart up the ramp?


List 6 Simple Machines


What is the weight in Newtons of a box that has a mass of 243.5 kg?


A base ball is thrown with a velocity of 155 m/s if the baseball has a mass of .4kg what is the KE?

An onlympic diver is on a platform 10 M above the pool. his weight is 646 Newtons. What is the diver's mass?

What is the divers PE?

A rock has off a ledge that is 325.5 M high it has fallen 215.6 M the PE of the rock was 1,435,455 J.

How fast is it falling
What is its current PE
What will be the rocks Final Velocity
What is the mass of the rock
How long has it been falling?

Answer 1

Recall that work is force time distance. But there's a neat trick to problems involving height. Assuming that friction is very small, the work done is exactly the height times mass times the gravitational acceleration, or Weight * Height,so:

Weight(250N)*4=1000Joules (this is how we express work when we use Newtons and meters).

The effort all depends on the angle of the ramp. If he were to go straight up, he'd have to expend 250newtons, the object's weight, up 4 meters. That's a lot. But if we move up a longer incline, we reduce the force even though the work stays the same. The reason we do this is that we want to be able to handle less effort, even though it takes us longer time.

What we need to do is determine what proportion of the Weight is parallel to the surface of the incline. This will be the actual Weight that the person doing the pushing experiences.


We can use the Pythagorean Theorem here to first determine the angle of incline. Since the height of the triangle formed by the incline is 4 and the incline itself (which is the hypotenuse) is 16, the sine (opposite/hypotenuse) is 4/16, or .25. The inverse sine of this gives us an angle of 14.48 degrees.

We want to know the force that is parallel to the incline. We find this by multiplying the Weight by the sine of the 14.48 angle, or

250*sine 14.48=62.5

6 machines:

-a pulley
-a lever
etc

Weight is just mass * acceleration of gravity, which is about 10m/s^2. So 243.5*10=2435 Newtons

You can check the accuracy here by realizing that the work stays the same, even though the Force applied and distance changes: 62.5N*16meters=1000Joules.

KE= 1/2(mass*velocity-squared)=

.5(.4kg*155m/s)=31Joules

Weight is simply mass times gravity, so if he weighs
646N, 646N/10=64Kg
PE=mgh=64*10*10=6400Newtons
If the rock initially had 1,435,455Joules of potential energy, it weighed 1,435,455/325.5=4410N
Incidentally since the rock weighs 4410Newtons, its mass is simply the weight divided by gravitational acceleration, or
4410/10=441Kg

As it fell, the rock lost height above ground, and therefore potential energy. It lost (325.5-215.6)=110meters in height, which translates to 110*4410N=485100Joules. This is the energy it lost, but that means we still have 1,435,455-485,100=950,355Joules at 215.6meters above ground (this is the current PE).

Acceleration is meters/second-squared. So what we want to find is what the current speed is. If it starts from 0, and falls 110 meters, we have:

We can use the formula for distance, which is:

y= v(original)*time+1/2acceleration*time-squared

The y tells us how far the rock has fallen, the acceleration is the acceleration due to gravity, about 10m/s^2. The time we don't know yet, but we'll find out.

110=0*t(it had no initial velocity since it fell from rest) +1/2(10t^2)
220=10t^2
22=t^2
solving for t we have t=4.69 seconds. It has been falling for this amount of time.
Since we started from rest, the final velocity is simply the acceleration (here 10) multiplied by the time, here 4.69. We get a velocity of 46.9, or about 47 meters/second.

Answer 2

1.A man pushes a cart up a ramp thats is 4 meters high and 16 meters long. The cart weights 250 Newtons. How much work was done?

Question asks for Work,Work is simply the amount of force that
is required to move an object a particular distance.The formula for work is W=F.D.CosÓ© where F=force, D=distance and W=work and CosÓ©=angle at which work is being done. You use Pythagorean theorem to find the CosÓ© angle and distance pushed up the ramp.

Pythagorean Theorem

|\
| \
4m | \
|_ _ \
16m
I tried my best to draw the triangle diagram, if you need a better picture go to:

http://i15.tinypic.com/2rmsglf.png


In this question you have height 4m, base 16m Hypotenuse=?, find the hypotenuse(slant side) of triangle, by

Hypotenuse=square root (height^2 + base^2).
Hypotenuse=square root (4^2 + 16^2)=16.49m

This is the distance pushed up the ramp. You see the object is being pushed up the ramp, and there is an angle involved, you would find this angle using identity tanÓ©=height / base and the answer you would get you would take its inverse tan to get the angle at which object was pushed that 16.49 cm.In this case, tan Ó©=4cm/16cm=0.25, to find the angle Ó© you would take inverse tan of 0.25 on calculator which is 14.03 degrees. How to take Inverse tan? You would have to look that up on your scientific calculator manual. Usually it's (punch in 0.25 and then press shift and then tan and then equal sign to get angle) or in other calculators (punch in 0.25 and then press 2nd and tan and then equal sign to get angle). If using Windows Calculator simply go to View-->scientific, and check "inv" box, and punch in 0.25 and press tan to get the angle.

Now put everything in formula and solve

W=250N(16.49m)(cos 14.03)=3999.52 Joules [Up at angle of 14 degrees].

You put in these brackets [angle at which you push box up its same angle whose cos you take]

Therefore, 3999.52 Joules of Work is required to push box up the ramp.


b) Effort to push box up the ramp

Effort is simply amount of force in Newton required to push something up the ramp, in this case the effort is 250N because thats the amount of force required to push it up the ramp

2. Six Simple Machines are those machines that make work easier by allowing user to apply less force and cover greater distance. These machines=very simple and have few moving parts

-Lever(ex. hammer)
-Ramp (ex.similar to ramp used in work example)
-Wheel and Axle (ex/Cars wheel)
-Screw (ex.similar to a screwdriver)
-Wedge (ex.Wedge used to hold door in place)
-Pulley (ex. pulley used to pull clothes)


3. Weight in Newtons of a 243.5g object

Basically weight is force of gravity pulling on an object. The weight is expressed in newtons and given by formula F=m.g where m=mass in kg, and g=9.8 (gravity constant on earth) so plug in numbers. Remember to convert g to kg by 243.5/1000=.243kg,

F=mg , F=0.2435kg(9.8)=2.387N

4.A base ball is thrown with a velocity of 155 m/s if the baseball has a mass of .4kg what is the KE?

KE=1/2mv^2 where m=mass, v=velocity in m/s

m=0.4kg
v=155 m/s
K.E=1/2(0.4kg)(155m/s)^2=4805 N

Therefore, KE is 4805 N

5. An olympic diver is on a platform 10 M above the pool. his weight is 646 Newtons.

a) What is the diver's mass?

Weight is key word , and weight is 646 N, refer to question 3. F=m.g rite !!! F=646N, m=? , g=9.8 (earth gravity constant), solve for m.

F/g=m, 646N/9.8=m, m=65.9kg

Therefore, Weight of the diver is 65.9kg

b) Potential energy (PE)?

PE=m.g.h where m=mass, g=9.8 gravity constant, h=height
PE=(65.9kg)(9.8)(10m)=6460 Joules

So PE of diver is 6460 joules

6.A rock has fallen off a ledge that is 325.5 M high it has fallen 215.6 M the PE of the rock was 1,435,455 J.

a)How fast is it falling
V=? m/s

-PE=KE (Energy is conserved so potential and kinetic energy are same)..Suppose KE=1,435,455J

-KE=1/2mv^2 ... We require the mass of the rock first? We already have the KE to get mass use equation PE=m.g.h where m=? , g=9.8 (gravity constant), h=215.5m

PE/g.h=m plug in values, m=1435455/9.8(215.6)=679.3kg

So mass is 679.3kg, now find v=?

v=sq root (2.KE/m)
v=sq root[ 2 x 1,435,455 J/ (679.3g) ]=65m/s

Therefore rock is falling at 65m/s

b)What is its current PE

Current PE=m.g.h
m=679.3kg, g=9.8 (gravity constant), h=325.5-215.6=109.9m

Potential energy is in reference to height of rock to the ground, we subtracted the two heights(325.5m-215.6m=109.9m) to find out how much far from ground the rock is.

PE=m.g.h=679.3x9.8x109.9=731619.7 joules

c)What will be the rocks Final Velocity

Again suppose that PE=KE, the rocks potential energy will convert to kinetic as its falling down

Vf=?
m=679.3g
KE=731619.7 joules

v=sq root (2.KE/m)
v=sq root[ 2 x 731619.7 J/ (679.3g) ]=46m/s

So the rocks final velocity as it makes the last 109.9 meters of its journey is 46m/s

d)What is the mass of the rock?

The mass of rock is 679.3 g , this mass was calculated in part a of this question

e) How long has it been falling?

vf^2=vi^2+2ad where a=acceleration, d=distance, vf=final velocity, and vi=initial velocity, we have to find in this case acceleration. We know vf=46m/s , vi=65m/s, a=? , d=325.5m

vf^2 - vi^2 / 2(d) = a

a= 46^2 - 65^2 / 2 (325.5m) =-3.23 m/s^2

Therefore, acceleration is -3.23 m/s^2. Acceleration can be negative if its negative it means the object is slowing down, in this case rock is slowing down as it comes closer to ground which makes sense. To find the time substitute this and everything else into equation vf=vi+at , vf=46m/s, vi=65m/s, t=? , a= -3.23 m/s^2

t= Vf-Vi/ a = 40m/s-65m/s/(-3.23m/s^2)=7.7 seconds.

Therefore, the rock has been falling 7.7 seconds

I provided full and detailed explanation , because Physics is not just calculations its "why" and "how" you do the calculations.This separates Physics from Mathematics. Good Luck with your Homework.