A) <u>Weight = mass × acceleration (due to gravity) </u>
= 60×9.8
= 588 N
<u>B) Potential energy = mass x gravity x change in height
</u>
1,000 = 60.0 x 9.8 x h
h = 1.7 m
<u>C) Kinetic energyF = potential energyI
</u>
KEF = 1/2mv2
PEI = mgh = 1,000 J
1/2mv2 = 1,000
1/2(60.0)v2 = 1,000
v2 = 33.33
v = 5.77 m/s
Explanation:
(a) Hooke's law:
F = kx
7.50 N = k (0.0300 m)
k = 250 N/m
(b) Angular frequency:
ω = √(k/m)
ω = √((250 N/m) / (0.500 kg))
ω = 22.4 rad/s
Frequency:
f = ω / (2π)
f = 3.56 cycles/s
Period:
T = 1/f
T = 0.281 s
(c) EE = ½ kx²
EE = ½ (250 N/m) (0.0500 m)²
EE = 0.313 J
(d) A = 0.0500 m
(e) vmax = Aω
vmax = (0.0500 m) (22.4 rad/s)
vmax = 1.12 m/s
amax = Aω²
amax = (0.0500 m) (22.4 rad/s)²
amax = 25.0 m/s²
(f) x = A cos(ωt)
x = (0.0500 m) cos(22.4 rad/s × 0.500 s)
x = 0.00919 m
(g) v = dx/dt = -Aω sin(ωt)
v = -(0.0500 m) (22.4 rad/s) sin(22.4 rad/s × 0.500 s)
v = -1.10 m/s
a = dv/dt = -Aω² cos(ωt)
a = -(0.0500 m) (22.4 rad/s)² cos(22.4 rad/s × 0.500 s)
a = -4.59 m/s²
Personally I feel that never trying is worse because at least when you fail you know what you need to improve on and that way you at least get some closure. Where as when you never try it you would never know whether or not you were able to do it
