What is the physical representation of the area under a force versus extension or compression curve?
1 answer:
The compression curve would be theoretically given for a system of bodies in which the spring applies the force (Although in the same way the following process can be extrapolated to any system, depending on the type of Force to consider) For a spring mass system, the strength is given by Hooke's law as
Where,
K = Spring constant
x = Displacement
If we integrate based on distance we would have
This integral represents the area under the Force Curve based on each distance segment traveled.
This is the same formula that represents the elastic potential energy of a body. Therefore the correct answer is D.
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Answer:
The required angle is (90-25)° = 65°
Explanation:
The given motion is an example of projectile motion.
Let 'v' be the initial velocity and '∅' be the angle of projection.
Let 't' be the time taken for complete motion.
Let 'g' be the acceleration due to gravity
Taking components of velocity in horizontal(x) and vertical(y) direction.
= v cos(∅)
= v sin(∅)
We know that for a projectile motion,
t =
Since there is no force acting on the golf ball in horizonal direction.
Total distance(d) covered in horizontal direction is -
d = ×t = vcos(∅)×
=
.
If the golf ball has to travel the same distance 'd' for same initital velocity v = 23m/s , then the above equation should have 2 solutions of initial angle 'α' and 'β' such that -
α +β = 90° as-
d = =
=
=
.
∴ For the initial angles 'α' or 'β' , total horizontal distance 'd' travelled remains the same.
∴ If α = 25° , then
β = 90-25 = 65°
∴ The required angle is 65°.
Answer:
368224.29906 m/s
Explanation:
M = Mass of Polonium nucleus = 214 u
V = Velocity of nucleus
m = Mass of Helium nucleus = 4 u
v = Velocity of alpha particle =
In this system the momentum is conserved
The recoil speed of the nucleus that remains after the decay is 368224.29906 m/s