Answer:
a) = 258352.5J
b) = 23.63 m/s
c) = 1.8m
Explanation:
Data;
Mass = 925kg
Distance (s) = 28.5m
Force constant (k) = 8.0*10⁴ N/m
g = 9.8 m/s²
a) = work = force * distance
But force = mass * acceleration
Force = 925 * 9.8 = 9065N
Work = F * s = 9065 * 28.5 = 258352.5J
b) acceleration (a) = (v² - u²) / 2s
a = v² / 2s
v² = a * 2s
v² = 9.8 * (2 * 28.5)
v² = 9.8 * 57
v² = 558.6
v = √(558.6)
V = 23.63 m/s
C). The work stops when the work done to raise the spring equals the work done to stop it by the spring
W = ½kx²
258352.5 = ½ * 8.0*10⁴ * x²
(2 * 258352.5) = 8.0*10⁴x²
516705 = 8.0*10⁴x²
X² = 516705 / 8.0*10⁴
X² = 6.46
X = √(6.46)
X = 2.54m
The compression was about 2.54m
Answer:
a) The work done by gravity on the elevator is 258352.5 J
b) The speed of the elevator just before striking the spring is 23.63 m/s
c) The amount the spring compresses is 2.7 m
Explanation:
a) The work is equal to:
[tex]W=Fdcos\theta \\W=mgdcos\theta[/tex]
Where
m = 925 kg
g = 9.8 m/s²
d = 28.5 m
θ = 0°
Replacing:
[tex]W=925*9.8*28.5*cos0=258352.5J[/tex]
b) The work done by gravity on the elevator is equal to the change of kinetic energy:
W = ΔEk
[tex]W=\frac{1}{2} mv^{2} -0[/tex]
The velocity is:
[tex]v=\sqrt{\frac{2W}{m} } =\sqrt{\frac{2*258352.5}{925} } =23.63m/s[/tex]
c) The total work is equal to the sum to of the change of kinetic energy and the spring:
[tex]W_{g} +W_{spring} =0\\\frac{k}{2} x^{2} -(mg)x-mgd=0\\x=\frac{mg+-\sqrt{m^{2} g^{2}+2kmgd } }{k}[/tex]
Replacing:
[tex]x=\frac{925*9.8+-\sqrt{925^{2}*9.8^{2}+(2*8x10^{4}*925*9.8*28.5) } }{8x10^{4} } =2.7m[/tex]
