Answer:
WD = 11328 J → 1.1 × 10⁴ (to 2 sig figs)
Step-by-step explanation:
WD = work done (J)
F = force (N), i.e. the normal force on the person
W = weight (N)
s = displacement (m)
m = mass (kg) = 60
a = acceleration (m/s²) = 2
g = gravity (m/s²) = 9.8
t = time (s) = 4
u = initial velocity (m/s) = 0
The formulas or equations that are relevant ate:
WD = F × s
F = m × a
W = m × g → note: this is simply a variation of the formula F = ma
s = ut + ¹/₂.at²
We want to find WD, so we need to know the force and the displacement (or distance);
Firstly, we want to find the normal force on the person in the elevator;
The downwards force the person produces on the elevator is the weight of the person, which is:
W = 60 × g
W = 60 × 9.8
W = 588
We are told the elevator is accelerating upward, so we can construct an equation to find F with the formula F = ma:
F - W = 60 × 2
F - 588 = 120
F = 708
Note: illustrations may be helpful to understand this, as has been shown in the picture
We also need displacement, which we use the formula s = ut + ¹/₂at²:
s = 0(4) + ¹/₂(2)(4)²
s = 16 m
Now we have F and s, we can calculate WD:
WD = 708 × 16
WD = 11328 J → This can be rounded to 1.1 × 10⁴ to 2 significant figures