Answer:
Explanation:
a) 1.00 - 0.12 = 0.88
m = 1200(0.88)^t
b) t = ln(m/1200) / ln(0.88)
c) m = 1200(0.88)^10 = 334.20 g
d) t = ln(10/1200) / ln(0.88) = 37.451... = 37 s
e) t = ln(1/1200) / ln(0.88) = 55.463... = 55 s
C, at this moment it is directly 90 degrees to the right and is only travelling downwards
Answer:
-2.478
0.379
11.14
24.78
Explanation:
Angular frequency of spring in harmonic motion is given by?
ω = √(k/m)
ω = √(10/2.2)
ω = √4.54
ω = 2.13 s^-1
If at t=0 the mass is in negative amplitude (x = -A = -2.48 m) then we describe the position with negative cosine
x(t) = -A * cos(ωt)
x(t) = -2.48 * cos(2.13 * 1)
x(t) = -2.48 * 0.9993
x(t) = -2.478
Velocity and acceleration are 1st and 2nd derivative of position
b)
v(t) = Aω * sin(ωt)
v(t) = 2.48 * 2.13 * sin(2.13 * 1)
v(t) = 5.282 * sin2.13
v(t) = 5.282 * 0.03717
v(t) = 0.379 m/s
c)
a(t) = Aω^2 * cos(ωt)
a(t) = 2.48 * 2.12² * cos(2.13 * 1)
a(t) = 2.48 * 4.494 * cos2.13
a(t) = 11.15 * 0.9993
a(t) = 11.14 m/s²
d)
F = -k * x(t)
F = -10 * -2.478
F = 24.78 N
