i points A spring is hanging down from the ceiling, and an object of mass m is a

Question

i points A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T -2were is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct? When showing your work to turn in, make sure to show that you found the unit of k using dimensional analysis rather than by looking it up. Show (in the work you turn in) that this is equivalent to the units of N/m. This answer has not been graded yet. 2 2- 2 2- .C

Explanation / Answer

Question 1

T=2*pi*sqrt(m/k)

dimension of T=sec

dimension of 2*pi=nil(dimensionless)

dimension of m=kg

equation dimension

sec=sqrt(kg/k)

sec^2=kg/k

k=kg/sec^2

so dimension of k will be

MT^(-2)

dimension of N/m=kgms^(-2)/m=kgs^(-2) so it is same

Question 2

F=Gm1*m2/r^2

Dimension of F=MLT^(-2)

MLT^(-2)=G*M*M/L^2

G=ML^3T^(-2)/M^2=M^(-1)L^(3)T^(-2)

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