Question

How is momentum related to force?

Answer 1

For example for this question

Which would take more force to stop in 10 seconds: an 8.0-kilogram ball rolling in a straight line at a speed of 0.2 m/sec or a 4.0
kilogram ball rolling along the same path at a speed of 1.0 m/sec?

Answer 2

i like your questions.
it means you are trying to go deep into the the concept...
momentum is quantity of motion possessed by a body whereas force is the rate of change of momentum.

Answer 3

for eg.- suppose a truck and a car are moving on a straight line path with equal velocity.
the truck would have a greater momentum than that of a car.
momentum= mass*velocity
suppose superman wants to stop the truck & car from the front with his stretched hands.
so superman would have to apply more strength on truck to stop it in a given time 't' as compared to car for the same time 't'.
this strength applied would cause a change in momentum as velocity is changed from 'v' to zero.
thus bigger the change in momentum, bigger is the force applied & small the change in momentum, small the force applied.
force=( m*v-m*u)/t =m*(v-u)/t {where v-final velocity & u-final velocity}
now (v-u)/t=acceleration (ie. rate of change of velocity)

Answer 4

now more is the change in velocity in a given time, more is the change in momentum. thus more is the force applied and vice-verse.
this is the relation among velocity, momentum and force.

Answer 5

now, according to your question,
for ball of mass 8 kg,
momentum when body stopped= m*v=0
initial momentum of body= m*u= 8kg*0.2 m/s= 1.6 kg m/s
hence, force applied= (m*v-m*u)/t= (0-1.6)/10= -0.16 kg m/\[s ^{2}\]= -0.16N {negative sign shows force applied opposite to the motion of body}
similarly for ball of mass 4 kg,
force= (m*v-m*u)/t= (0-4)/10= -0.4N
force on ball 'b'> force applied on ball 'a'

Answer 6

in the third box, u-initial velocity

Answer 7

Ok question what exactly is "u"? I liked the super man analogy btw it helped!

Answer 8

u is the velocity when we start observing the motion of the body

Answer 9

I might be asking a lot of questions because I need to understand this:

so for momentum when you say quantity of motion are you saying how much it's moving ? Like the velocity of the body?

Answer 10

algebraically momentum (p) is related to force F in the following:
\[p=mv \\\Delta p=F\Delta t\\F=\frac{dp}{dt}\\ \Delta p = \int_{t_1}^{t_2}F(t) dt\\ F=\frac{dv}{dt}m=ma\]

Answer 11

agreene why are you introducing the concept of calculus for a child who has just got to know about the concept of momentum

Answer 12

to dareintheren
yes it means the same

Answer 13

velocity is independent of mass...
velocity is the rate of change of distance or you can say distance traveled by a body per unit time...
but for momentum, it includes both mass and velocity.

Answer 14

for eg.- for a truck, even if it moving with a slow speed, its momentum would be high as compared to a bike or a car because the mass of truck is so great.

Answer 15

Ok ok thanks!!, could you explain the second post you made where you typed the formulas? I hope I'm not keeping you from anything ..

Answer 16

if a truck and car moving with same speed collide then due to the huge momentum of truck , truck would move in the same direction of its motion which was before the collision but the car has to move in the direction of the motion of truck after collision....just visualize!!!

Answer 17

see momentum is mass multiplied by velocity...
so when we started observing the motion of body, the mass is m and inital velocity is u, hence momentum would be m*u
and when the momentum is changed, the mass would remain constant but the velocity would change & let it be v which is final velocity.
so change in momentum is mv-mu, which is in time t & caused by the force f

Answer 18

thus f=(mv-mu)/t

Answer 19

have you read the 2 posts that i have written now

Answer 20

ok you are not able to visualize the collision of truck & car...
just think how a car is crushed under a truck...
it is due to the momentum of the truck that the car 's momentum was not able to tolerate....

Answer 21

have you deleted your post, it was a bit wrong as acceleration is change in velocity per unit time....

Answer 22

going offline bye!!!