So the person weighs 65kg, and 9.4% of that is head, so 65*0.094 = 6.11 kg is the mass of the head. If we deaccelerate from 40 m/s to 0 m/s in 0.2 s, our total acceleration is: a = Δv/Δt = (0 - 40)/(0.2 - 0) = -200 m/s². We can then use Newton's second law, F = ma, to find the force, using m as mass of the head and a as our acceleration (we'll ignore the negative sign because we don't care about the force's direction here). F = ma = (6.11)(200) = 1222 N, a pretty large amount of force.
It now occurs to me that the easier way to do this, though slightly more advanced, is to use that Force is the derivative of momentum, or F = dp/dt, or with no calculus, F = Δp/Δt, where p is momentum and t is time. p = mv, where m is mass and v is velocity, so F = Δp/Δt = Δ(mv)/Δt = ((6.11)(0) - (6.11)(40))/(0.2 - 0) = (6.11)(40)/(0.2) = 1222 N. So yeah it's quicker, I feel this is less straight forward though.
Answer:
Same direction to produce maximum magnitude and opposite direction to produce minimum magnitude
Explanation:
Let a be the angle between vectors A and B. Generally when we add A to B, we can split A into 2 sub vectors, 1 parallel to B and the other perpendicular to B.
Also let A and B be the magnitude of vector A and B, respectively.
We have the parallel component after addition be
Acos(a) + B
And the perpendicular component after addition be
Asin(a)
The magnitude of the resulting vector would be
As A and B are fixed, the equation above is maximum when cos(a) = 1, meaning a = 0 degree and vector A and B are in the same direction, and minimum with cos(a) = -1, meaning a = 180 degree and vector A and B are in opposite direction.
Missing part of the text:
"Two masses, m1 = 2.12 kg and m2 = 9.01 kg are on a horizontal frictionless surface and they are connected together with a rope as shown in the figure."
and missing figure (see attachment)
Solution:
We can write Newton's second law for the whole system m1-m2 and for m2 only (2 equations). Only one force (F) acts on the m1-m2 system, while if we consider m2 only we have two forces acting on it: F and T (tension), in the opposite direction. So, the two equations are
where a is the acceleration of the system.
From the first equation we get
and substituting it inside the second equation, we get
re-arranging, we get
Using
,
, and using the maximum value of T that is allowed not to break the rope (T=55 N), we can find the maximum allowed value for F:
?.............................
Answer:
17.2 meters
Explanation:
Carbon dioxide (CO2) molecular mass is 44g/mol, then the number of moles of 10000kg carbon dioxide will be:
10,000kg * (1000g/kg)/ (44g/mol) = 227,272moles
The volume of gas in STP is 22.4 L/mol, then the volume of the carbon dioxide will be:
227,272 moles* 22.4L/mol= 5,090,909 L
One liter equal to 0.001 meter cubic. The formula for cube volume is , if the volume is 5090909L then the side of the cube will be:
volume=
5090909L * (0.001 /L)=
side=
side= 17.2m