Block oscillating on an inclined plane Must answer both parts. A block of weight
ID: 1480086 • Letter: B
Question
Block oscillating on an inclined plane
Must answer both parts.
A block of weight W = 23 N, which can slide without friction on a 22.5° incline, is connected to the top of the incline by a massless spring of unstretched length xo = 0.6 m and spring constant k = 275 N/m. Part A: By how much will the spring be stretched when the system is in equilibrium?
Part B: If the block is pulled slightly down the incline from its equilibrium position and released, what is the frequency of the ensuing oscillations?
thank you!
Explanation / Answer
the stretched length of the spring is calculated as follows:
W*sin theta = kx
x = W*sin theta /k
= 23*sin22.5 /275
= 0.032 m
= 3.2 cm
period is calculated as follows:
T =2*pisqrt[m/k] = 2*pi*sqrt[(23/9.8)/275] = 0.3695 s
hence, the frequency is,
f = 1/T = 2.7 Hz