T is in seconds (s)
<span>2pi is dimensionless </span>
<span>L is in meters (m) </span>
<span>g is in meters per second squared (m/s^2) </span>
<span>so you can write the equation for the period of the simple pendulum in its units... </span>
<span>s=sqrt(m/(m/s^2)) </span>
<span>simplify</span>
<span>s=sqrt(m*s^2*1/m) cancelling the m's </span>
<span>s=sqrt(s^2) </span>
<span>s=s </span>
<span>therefore the dimensions on the left side of the equation are equal to the dimensions on the right side of the equation.</span>
Answer:
Explanation:
Change in length of spring = 2.13 m
Component of weight acting on spring = mg sinθ
so
mg sinθ = k x where k is spring constant and x is total stretch due to force on the spring.
Here x = 2.13
mg sin17 = k x 2.13
31 x 9.8 sin17 = k x 2.13
k = 41.7 N/m
b ) In case surface had friction , spring would have stretched by less distance .
It is so because , the work done by gravity in stretching down is stored as potential energy in spring . In case of dissipative force like friction , it also takes up some energy in the form of heat etc so spring stretches less.
The answer is A. Force is equal to mass x acceleration. The acceleration due to gravity is a constant so multiplying the mass by 2 would double the force.
