<span># of protons + # of neutrons = atomic mass</span>
Answer:
See explanation below.
Explanation:
For this case we atart fom the proportional model given by the following differential equation:
And if we rewrite this expression we got:
If we integrate both sides we got:
And using exponential on both sides we got:
Where represent the initial amount for the isotope and t the time in years and A the amount remaining.
If we want to apply a model for the half life we know that after some time definfd the amount remaining is the hal, so if we apply this we got:
We can cancel and we got:
If we solve for k we can apply natural log on both sides and we got:
And that would be our proportional constant on this case.
If we replace this value for k int our model we will see that:
And using properties of logs we can rewrite this like that:
And thats the common formula used for the helf life time.
Answer:
90.3125 m
Explanation:
a = 10m/s^2 (constant)
S=height
U=initial velocity
a= gravitational acceleration
t= time
s = 0 + 1/2 * 10 * 4.25 ^2
u is 0 because it is dropped without velocity
s =90.3125 m
Answer:
6.57 m/s
Explanation:
First use Hook's Law to determine the F the compressed spring acts on the mass. Hook's Law F=kx; F=force, k=stiffnes of spring (or spring constant), x=displacement
F=kx; F=180(.3) = 54 N
Next from Newton's second law find the acceleration of the mass.
Newton's .2nd law F=ma; a=F/m ; a=54/.75 = 72m/s²
Now use the kinematic equation for velocity (or speed)
v₂²= v₀² + 2a(x₂-x₀); v₂=final velocity; v₀=initial velocity; a=acceleration; x₂=final displacement; x₀=initial displacment.
v₀=0, since the mass is at rest before we release it
a=72 m/s² (from above)
x₀=0 as the start position already compressed
x₂=0.3m (this puts the spring back to it's natural length)
v₂²= 0 + 2(72)(0.3) = 43.2 m²/s²
v₂= = 6.57 m/s
If there is no friction, then NO force is needed to keep an object moving. Go back and look at Newton's first law of motion again.