A high-speed lifting mechanism supports an 800kg object with a steel cable that is 25 m long and...?

Question

4.00 cm2 in cross-sectional area. A) Determine the elongation of the cable. B) By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 3 m/s2? C) What is the greatest mass that can be accelerated upward at 3 m/s2 if the stress in the cable is not to exceed the elastic limit of the cable, 2.2 x 108 Pa?

I've worked out the problems below but I'm not sure if I did the calculations correctly. If you see an blatant errors, please point them out. Thank you :)

A) F/A= Y(Change in L)/ L
800 kg = 7840 N
7840 N/ 4 x 10^-4 m^2 = (20 x 10^10 Pa)(change in L)/ 25.0 m
Change in L = 2.45 mm
B) F=(mass)(acceleration)
F=(3.0 m/s^2)(800 kg) = 2400 N
F/A= Y(Change in L)/ L
2400 N/ 4 x 10^-4 m^2 = (20 x 10^10 pa)(change in L)/ 25 m
change in L = 0.75 mm
C) F=mass x acceleration
F= (3.0 m/s^2)m
F/A = 2.2 x 10^8 Pa
(3.0 m/s^2)m / (4 x 10^-4 m^2) = 2.2 x 10^8 Pa
m = 29333.3 kg

Answer 1

Looks like you didn't add g (grav. acc.) in B and C.
Assuming 20 x 10^10 Pa is the Young's modulus, everything else looks OK.

Answer 2

for C)

I think you need to take into account of the original weight of the object along with the upward acceleration. So. F = m * (3.0 m/s^2 + 9.8 m/s^2) and not just m * 3.0 m/s^2

=)