I was studying Dynamics and came across a problem I could not solve. It was an exercise about the law which stipulates the sum of the momentums in an isolated system stays the same at all times.
So m1 x v1 + m2 x v2 ... = m1 x v'1 + m2 x v'2...
A wagon weights 20 tons (20'000 kg). Calculate the force that needs to be applied to it so that in one minute, its speed attains 54 km/h?
I would use the formula as 20 tons x 0 km/h = 20 tons x 54 km/h - ? kg x ? km/h. This would mean the momentum of the wagon at rest = momentum of the wagon moving minus the momentum of something which I cannot figure out...
So we can say 20'000 kg x 54 km/h = ? kg x ? km/h. The problem is I'm not sure what I'm doing, and I can't seem to figure out where the force in Newtons is supposed to be in this formula.
Help?
So m1 x v1 + m2 x v2 ... = m1 x v'1 + m2 x v'2...
A wagon weights 20 tons (20'000 kg). Calculate the force that needs to be applied to it so that in one minute, its speed attains 54 km/h?
I would use the formula as 20 tons x 0 km/h = 20 tons x 54 km/h - ? kg x ? km/h. This would mean the momentum of the wagon at rest = momentum of the wagon moving minus the momentum of something which I cannot figure out...
So we can say 20'000 kg x 54 km/h = ? kg x ? km/h. The problem is I'm not sure what I'm doing, and I can't seem to figure out where the force in Newtons is supposed to be in this formula.
Help?
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Your formula@
m1 x v1 + m2 x v2 ... = m1 x v'1 + m2 x v'2...
has nothing to do with this problem It is usually used when 2 or more objects collide, to help. work out their velocities after the collision.
The wagon doesn't 'weigh' 20000kg, that's its mass. Weight is a force (measured in newtons).
You have to work in consistent units or none of the equations work. Use SI units.
_______________________
1 minute = 60s
54km/h = 54000m/3600s = 15m/s
________________
Method 1: Impulse (force x time) = change of momentum
Since the wagon starts from rest, change of momentum = 2000x15
Ft = mv
F x 60 = 20000 x 15
F = 20000 x 15/ 60
= 5000N
_______________
Method 2 Force = mass x acceleration
Acceleration = 15/60
= 0.25m/s²
F = ma
= 20000 x 0.25
= 5000N
m1 x v1 + m2 x v2 ... = m1 x v'1 + m2 x v'2...
has nothing to do with this problem It is usually used when 2 or more objects collide, to help. work out their velocities after the collision.
The wagon doesn't 'weigh' 20000kg, that's its mass. Weight is a force (measured in newtons).
You have to work in consistent units or none of the equations work. Use SI units.
_______________________
1 minute = 60s
54km/h = 54000m/3600s = 15m/s
________________
Method 1: Impulse (force x time) = change of momentum
Since the wagon starts from rest, change of momentum = 2000x15
Ft = mv
F x 60 = 20000 x 15
F = 20000 x 15/ 60
= 5000N
_______________
Method 2 Force = mass x acceleration
Acceleration = 15/60
= 0.25m/s²
F = ma
= 20000 x 0.25
= 5000N