Force & Work Done?

Question

A car with mass 1000kg is moving down the road at 14m/s. Calculate the Kinetic energy of the car, momentum of the car.
If the car comes to a sudden stop over a distance of 2 meters, what is the average force applied to the car? How much work done by the car? Where did the energy go?
Help anyone???

Answer 1

Kinetic Energy, KE:
KE=1/2mv^2
Substitute known values:
KE=1/2*1000*14^2 Joules
= 98,000J

Momentum=mv
=1000*14
=14000 kgm/s

Work= F*s, where F is the average force in N, and s is the displacement in m.

Substitute known values:

Work=F*2

Based on the principle of conservation of energy:

KE=Work

Substitute:

98000=F*2
F=98000/2
=49000 N

Work done:

F*s=49000*2
=98000J

The kinetic energy when the car stopped is equal to 0. It was transformed to work energy.

Answer 2

Calculating K.E of the car:

K.E = 1/2 X m X v2
K.E = 1/2 X 1000 X 14 X 14
K.E = 98000

Calculating momentum of the car:

Momentum (kgm/s) = mass (kg) x velocity (m/s)
Momentum = 1000 X 14
Momentum = 14000

Calculating Average Force Applied:
First, find the time taken for the car to stop. By drawing a distance-time graph, the formula for time taken is

1/2 X 14 X time = 2
time = 2/7

After finding the time, find the acceleration next. This is done using the formula accleration = change of velocity divided by time.

decceleration = (14-0) / (2/7)
decceleration = 49

(*NOTE: 49 is the value of deceleration, while -49 is the value for acceleration. Acceleration is a vector and the positive/negative signs indicate direction of force applied. Therefore state the direction you want taken as positive clearly in your actual working.)

Using ACCLERATION of -49,
F=ma
F= 1000 X -49
F= -49000

Calculating Work Done:
WD= F X D
WD= -49000 X 2
WD= -98000

(*NOTE: Leave the value of work done WITHOUT the negative sign, as Work Done is a SCALAR entity. Therefore, work done by the car was 98000Nm.)

Some of the energy was lost to overcome friction, while the rest was converted to other forms of energy such as heat and sound.

Hope that helped.

Answer 3

The kinetic energy lost = ½ m v v.

This is equal to the work done by the force = force x displacement =F x s.


Therefore, both work done and kinetic energy
= ½ m vv
= (½) 500 x 14 x 14 = 9700 joule.
Work done by the force = force x displacement =F x s

F = work done / displacement = 9700 joule / 2 meter = 4850 newton.

Since all its kinetic energy is lost it is converted into heat energy, sound energy etc.
The momentum of the car before stopping is M x v

1000 x 14 = 14 000 kg. m/ s

Answer 4

KE=1/2 mv^2=1/2 x 1000 x 14 x14 =98000 J
v=0
u=14 m/s
s=2
a=0-196/2 x 2=-49m/s ---retardation
F=ma=1000x49=49000 N
W=F.s=49000 x2=98000

Answer 5

kinetic energy,
K.E.= 0.5*m*v^2
=0.5*1000*14^2
=98000 J
momentum,
p=mv
=1000*14
=14000 kgm/s

F=ma

a=acceleration (unknown)
using the formula (v')^2=v^2-2as, a=49 m/s^2

F=1000*49=49000 N
Work done=Fs=49000*2=98000 N

the K.E. is turned into the energy necessary to change the state of inertia of the car

Answer 6

KE = .5 * mass * (velocity squared)
KE = .5 * 1000 * 14 * 14
KE = 98 000J

momentum (p)= mass * velocity
p = 1000 * 14
p = 14 000 kg m/s

Force = mass * acceleration
acceleration = velocity / time

i suggest you figure out the rest yourself, as I can't be bothered. =P
haha.

Oh and work done = Force * distance
That's pretty easy.

GO FOR IT!

=D

Answer 7

K.E = 1000(14^2)/2
K.E = 98,000 J

p = (1000 kg)(14 m/sec)
p = 14,000 N-sec

K.E. = W = Fs
F = 98,000/2
F = 49,000 N

W = 98,000 J

The energy went into heat. Don't touch the brakes!