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Work

Work is said to be done when an applied

force, f moves an object thru a distance, d.

W = f x d

In the metric system,

the unit of force is in Newton (N),

unit of distance is in meters (m),

and the unit of work is in Joules (J).

Work

When force is applied

at an angle, θ, then only

the cosine component

of the force does work.

Then W = f d cos θ

Here again the unit of Work is in Joules (J).

Work due to non-constant force

Work done by a non-constant force can be calculated by finding the area under a Force-displacement graph.

Here the

area is a

triangle.

So,

W=(1/2)F.d

Gravitational Potential Energy

Work done by gravity (loss of height) and against gravity (gain of height) is called GPE.

{ w = fd, f = ma or f =mg (if gravity applies the force); so w = mgd or w = mgh)

Gravitational Potential Energy = mgh

Unit of m is kilograms (Kg)

“g” is acceleration due to gravity and on earth it is 9.8 or 10m/s2.

“h” is the height and is in meters (m)

Unit of GPE in metric system is Joules.

Kinetic Energy

It is the energy of motion

F=ma F=m(Vf-Vi)/t F=m (½)vavg/t

W=F x d W= m (½)vavg(d/t) = (½)mv2

KE= (½) mv2

In the metric system,

the mass is in kilograms (kg),

the velocity is in meters/second (m/s)

and KE is in Joules (J)

Work to KE

Work has to be done to make an object move.

Work = KE

F d = (½) mv2

This is conversion of work to KE.

Example: Throwing a ball.

You have to apply a force through a distance on a ball to make it move.

Work to GPE

Work has to be done to lift or drop an object.

Work = GPE

Fd = mgh

This is conversion of work to GPE.

Example: Lifting or dropping a ball.

You have to apply a force through a height (distance) on a ball to lift a ball.

Gravity applies a force through a height (distance) on a ball dropped from a height.

Units of work and/or Energy

- Unit of work or energy in Metric System is in Joules.
- Some times the unit of Energy can also be in KWh (Kilo-Watt-hour).
- Most Energy Companies use KWh. But here they mean electrical energy.

Conservation of energy (COE)

COE states that energy can transform from one form to another, but cannot be created or destroyed.

Let us take the example of a skate boarder

or the Bowling ball, or the Happy ball-Sad ball

Lab or the Toy car efficiency Lab.

TMEi = TMEf

TME stand for Total Mechanical Energy.

If we take the initial, “i” at the left extreme end and final, “f” in the middle, then we using TMEi = TMEf

We get PE = KE or mgh = (½) mv2

We can solve this problem, using _________.

m=2kg

30m

Find the velocity of the ball at the bottom of the hill.

Answer: _______

24 m/s

We can solve a similar problem using _______, even without knowing the mass of the object.

Because _______ cancels out on both sides.

Find speed of the ball at the bottom of the hill. Answer: ___________.

mass

50m

31.7 m/s

Similarly we can solve this by using this relationship __________________.

10m/s

Find the maximum height this ball can reach.

Answer: _______.

KE = GPE

5 m

Total Mechanical Energy

Total non Mechanical Energy

Kinetic Energy

Potential Energy

Gravitational

Elastic

Kinetic Energy

Potential Energy

Energy loss to friction

Gravitational

Elastic

Conservation of Energy, COE

- The total Mechanical Energy (TME) in a conservative system is conserved.

TMEi = TMEf

[PE + KE]before= [PE + KE]after

- The TME in a non-conservative system is not conserved (cannot be transformed). Some energy is lost as Thermal Energy due to friction.

[PE + KE]before= [PE + KE + Frictional losses]after

Problem 1 – Roller Coaster:

3m/s

60m

40m

15m

- Determine the velocity of a coaster at the top of the loop. Assume frictionless track.
- Using:
- Answer: ____________

PEi + KEi = PEf + KEf

20 m/s

Problem 2 – Pole Vault

8m/s

Determine the initial ground speed of this pole vaulter when she passes over the 10m high bar at the speed of 8m/s.

Using: , we get __________

KEi = PEf + KEf

16.2m/s

Problem 3 – Non conservative force

30m

A 40kg child sleds down the hill. Find his velocity at the bottom. Assume frictionless hill. If he hits packed snow and slows to speed of 10m/s, find energy lost to friction.

Power and its unit

Power = Work or Energy/Time

We have just learned that work done can be converted to KE or PE.

So Power = Work/time

Or Power = KE/Time

Or Power = PE/Time

Or Power = Total Energy/Time

Metric unit of Power is Watts.

1 Calories = 1kcalorie = 4186J

Horse power is also a unit of power and

1Hp = 746 Watts

Problem – Roller Coaster:

3m/s

60m

40m

15m

- Find the power of the motor that can lift a 500kg car to the top of the first hill in 10 sec.
- (Hint – remember that at the top of the first hill, the car has some speed also.)

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