Please answer this with a brief explanation. Thank you. A block with a mass of 0
ID: 1781954 • Letter: P
Question
Please answer this with a brief explanation. Thank you.
A block with a mass of 0.500 kg is connected to a spring, displaced in the positive direction a distance of 50.0 cm from equilibrium, and released from rest at t0. The block then oscillates without friction on a horizontal surface. After being released, the first time the block is a distance of 35.0 cm from equilibrium is at t = 0.200 s. (a) What is the block's period of oscillation? (b) What is the the value of the spring constant? N/m (c) what is the block's velocity at t = 0.200 s? (Indicate the direction with the sign of your answer.) m/s (d) what is the block's acceleration at t = 0.200 s? (Indicate the direction with the sign of your answer.) mVsExplanation / Answer
1/2 K ( 0.5^2) = 1/2 K (
Amplitude =0.5 m
m = 0,5 kg,
x = A cos ( wt)
0.35 = 0.5 cos ( 0.2w)
0.2 w= cos^-1 ( 0.35/0.5)
0.2 w= 45.57 radians
w= 227.86 radians/ S = sqroot ( k/m)
51922. 45 = K/ 0.5
K = 25961.2 N/m
T = 2pi/ w= 0.027 seconds apprx
v = -Aw sin (wt)
V = - 0.5 ( 227.86) sin ( 227.86 x 0.2)
V = 2.154 m/s
a = AW^2 cos (wt) = 0.5(227.86^2) cos ( 45.57)= 438.8 m/s^2