Please help me with #10, and #11. Two identical springs with spring constant k a
ID: 2101144 • Letter: P
Question
Please help me with #10, and #11.
Two identical springs with spring constant k are connected to identical masses M, as shown in the figures above. The ratio of the period for the springs connected in parallel (Figure 1) to the period for the springs connected in series (Figure 2) is A uniform disk with a mass of m and a radius of r rolls without slipping along a horizontal surface and ramp, as shown above. The disk has an initial velocity of upsilon. What is the maximum height h to which the center of mass of the disk rises?Explanation / Answer
10. For figure 1. both the strings will have same extension
So net spring force = 2kx
=> keff = 2k => T = 2piSqrt(m/2k)
For figure 2, Net spring force = k(x1 + x2)
=> keff = k
=> T = 2piSqrt(m/k)
=> T1 : T2 = 1/Sqrt(2)
So B is the correct answer
11. At any time v = wr
At lower level energy in the disc = Translational KE + Rotational KE
= 0.5 m v^2 + 0.5 I w^2
= 0.5 m v^2 + 0.5(0.5 m r^2) (v/r)^2 = 0.75*mv^2
Final energy = mgh
mgh= 0.75 mv^2
=> h = 3v^2/ 4g
(B) option is correct