Help With Simple Work and Energy Physics Problem?

Question

A cable with 19.0 N of tension pulls straight up on a 1.11 kg block that is initially at rest.

1) What is the block's speed after being lifted 3.30 m? Solve this problem using work and energy.

Answer 1

Net resultant upward force

= 19 - 1.11*9.8

= 8.122

Increase in kinetic energy = net work done

=> (1/2) mv^2 = 8.122 * 3.3

=> v^2 = (8.122*6.6) / 1.11

=> v = √[(8.122*6.6) / 1.11]

= 6.95 m/s.

Answer 2

3.30 * 19 = Fd = W = 62.7 joules of work = 62.7 joules of energy transfered.

This is equal to the energy of the block, right?

62.7 = PE  + KE

= mgh + .5mv^2

= m(gh + .5v^2)

56.49 = gh + .5v^2

= 33 + .5v^2

23.49 = .5v^2

v = 6.85 m/s