Answer to Question #241821 in Molecular Physics | Thermodynamics for Kelani

Question

A cable exerts a constant upward tension of magnitude 2.26 ✕ 10⁴ N on a 2.00 ✕ 10³ kg elevator as it rises through a vertical distance of 3.50 m.

(a) Find the work done by the tension force on the elevator (in J).

 

___ J

(b) Find the work done by the force of gravity on the elevator (in J).

 

 ___J

Answer 1

Tension in the string $T = 2.26 \times 10^4\; N$

mass of the elevator $m = 2.00 \times 10^3 \;kg$

the rise in vertical distance S = 3.5 m

Tension force will act upwards on the elevator

displacement is also upwards

Work done $W = FScos θ$ here θ = 0

$W_1 = (2.26 \times 10^4 \; N) \times (3.5) \times cos 0 \\ W_1 = 7.91 \times 10^4 \;Joules$

Work done by the tension force on the elevator $W_1 = 7.91 \times 10^4 \;J$

Now,

gravitational force $F_g = mg$

$F_g = 2.00 \times 10^3\; kg \times 9.81 \\ F_g = 1.962 \times 10^4 \; kg$

Work done is $W = FS cos θ$ here θ is 180 (force and displacement are in the opposite direction)

$W = 1.962 \times 10^4 \; kg \times 3.5 \times (-1) \\ W = -6.87 \times 10^4 \; Joules$

Work done by the gravitational force on the elevator $W_1 = -6.87 \times 10^4 \;J$