The greater the mass of an object, the greater its force due to gravity
1 answer:
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Explanation:
The momentum of the three objects are as follow :
11 kg-m/s, -65 kg-m/s and -100 kg-m/s
Before collision, the momentum of the system is :
After collison, they move together. It means it is a case of inelastic collision. In this type of collision, the momentum of the system remains conserved.
It would mean that, after collision, momentum of the system is equal to the initial momentum.
Hence, final momentum = -154 kg-m/s.
Answer:
Explanation:
Given that m= 1 slug and given that spring stretches by 2 feet so we can find the spring constant K
mg=k x
1 x 32= k x 2
K=16
And also give that damping force is 8 times the velocity so damping constant C=8.
We know that equation for spring mass system
my''+Cy'+Ky=F
Now by putting the values
1 y"+8 y'+ 16y=6 cos 4 t ----(1)
The general solution of equation Y=CF+IP
Lets assume that at steady state the equation of y will be
y(IP)=A cos 4t+ B sin 4t
To find the constant A and B we have to compare this equation with equation 1.
Now find y' and y" (by differentiate with respect to t)
y'= -4A sin 4t+4B cos 4t
y"=-16A cos 4t-16B sin 4t
Now put the values of y" , y' and y in equation 1
1 (-16A cos 4t-16B sin 4t)+8( -4A sin 4t+4B cos 4t)+16(A cos 4t+ B sin 4t)=6sin4 t
So by comparing the coefficient both sides
-16A+32B+16A=0 So B=0
-16 B-32 A+16B=6 So A=-3/16
y=-3/16 cos 4t
Now to find the CF of differential equation 1
y"+8 y'+ 16y=6 cos 4 t
Homogeneous version of above equation
So
So the general equation
Given that t=0 Y=0 So
t=0 Y'=0 So
The above equation is the general equation for motion.