What would happen to the the 5.98e24 kg Earth?

  • Thread starter Thread starter sensesfail
  • Start date Start date
  • Tags Tags
    Earth
AI Thread Summary
If 270 million people in the US jumped simultaneously, exerting an average force of 800 N each for 0.10 seconds, the total force exerted would be significant. The calculations show that the change in momentum for the Earth would equal the total momentum generated by the people. The formula p(e) = (270e6) * 800 * 0.1 is used to find the Earth's resulting velocity. The resulting velocity of Earth is extremely small, illustrating that despite the large number of people, the mass of Earth is so great that the impact is negligible. Overall, the exercise demonstrates the principles of momentum conservation in a closed system.
sensesfail
Messages
8
Reaction score
0

Homework Statement



If 270 million people in the US jumped in the air at simultaneously, pushing off Earth with an average force of 800 N each for a time of 0.10 seconds, what would happen to the the 5.98e24 kg Earth? Show calculation that justifies your answer.

Homework Equations



F = mv/t
p = mv

The Attempt at a Solution



F = 800 N
t = 0.10 s
m = 5.98e24 kg

800 = (5.98e24 * v) / 0.10

v = 1.3378 e -23

p = 5.98e24 * 1.3378e-23
p = 80 kg*m/s
 
Physics news on Phys.org
Thats almost right. You forgot the 270 million bit.
 
chaoseverlasting said:
Thats almost right. You forgot the 270 million bit.

so do i just times 270 mil by 80?
 
Not quite. F=dp/dt, dp=Fdt. Total change in momentum is zero for the system, therefore,
p(e)=p(people).

This gives p(e)=(270e6)*800*0.1. From this you find the velocity of earth.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Distance of geosynchronous satellite from earth
Replies
4
Views
2K
Tension on a Massive Rope: How to Calculate Tension at Different Points
Replies
11
Views
3K
Leakage of Air in a Spacecraft
Replies
16
Views
1K
Weight of person on Earth, and on a different planet's surface?
Replies
11
Views
2K
Circular Motion/Gravitational Acceleration Help Needed
Replies
5
Views
3K
Momentum of a ball bouncing off of the floor
Replies
13
Views
3K
Variation of gravitational attraction between Sun and Earth
Replies
3
Views
2K
Elastic Collision of Hydrogen and Carbon Atoms
Replies
9
Views
2K
Two sphere collision -- What's the speed?
Replies
6
Views
3K
Magnetic flux- is this the correct way to solve it?
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top