Please can you answer all three questions fully. Pleass provide explanations as
ID: 1604645 • Letter: P
Question
Please can you answer all three questions fully. Pleass provide explanations as well as all correct final units and equations . Thank you so much!
Two masses are shot at each other on a frictionless track using identical massless, ideal) springs, each with spring constant k. The left object has mass m. The right object has mass 4m. Each spring is compressed an identical distance x from its equilibrium length COCO m 4m 1. Derive an expression for the speed v of the mass m just after it leaves the spring. Let us know what principle of physics you are using and WHY (Newton's laws? Conservation of energy? Conservation of momentum? Something else?) Derive an expression for the speed, v4, of the mass 4m after it leaves the spring How does it compare to the speed of mass m? (Same? Half? Twice?...) 3. Choose a coordinate system. Draw a diagram representing the momentum of each mass. Which mass has the larger magnitude momentum? By what factor? (Show your work) In which direction (left or right) is the total momentum vector of the system (i.e. the system comprised of both masses m and 4m)?Explanation / Answer
1)
the spring is compressed by x
the spring mass system has elastic potential eneryg U = (1/2)*k*x^2
one the mass leaves the spring comes comes backs to
original length and elastic potential of the sytem
becomes zero .the mass gains kinetic energy
KE = (1/2)*m*v^2
from conservation of energy
total energy of a system is constant
(1/2)*k*x^2 = (1/2)*m*v^2
v = x*sqrt(k/m) = x(k/m)^(1/2)
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elastic potential energy = kinetic energy
(1/2)*k*x^2 = (1/2)*4m*v4^2
v4 = x*sqrt(k/4m)
v4 = (1/2)*x*sqrt(k/m)
v4 = v/2
v4 is half of v <<<<----answer
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momentum of mass m is P = m*v = m*x*sqrt(k/m) i
momentum of mass 4m is P4 = -m4*v4 = -4m*x/2*sqrt(k/m) = -2*m*x*sqrt(k/m) = -2*pi
mass 4m has larger magnitude momentum
P4 = 2p
momentum of 4m is 2 times momentum of m
total momentum Ptot = -m*x*sqrt(k/m) i
direction is to the left