Question

The diver finds a rectangular aluminum plate having dimensions 1.0m x 2.0m x 0.03m. A hoisting cable is lowered from the ship and the diver connects it to the plate. The density of aluminum is 2.7 x 103kg/m3. Ignore the effects of viscosity. (c) Calculate the tension in the cable if it lifts the plate upward at a slow, constant velocity. (d) Will the tension in the hoisting cable increase, decrease, or remain the same if the plate accelerates upward at 0.05 m/s2

Answer 1

Answer:

(c)Tension = 162 N

(d) Increase

Explanation:

(c)

In order for the cable to lift the plate at uniform velocity, the tension in the cable must be equal to the weight of the plate.

$Tension = Weight = (Density)(Volume)\\Tension = (2.7\ x 10^3\ kg/m^3)(1\ m)(2\ m)(0.03\ m)$

Tension = 162 N

(d)

The tension with upward acceleration will become:

$Tension = m(g+a)\\Tension = mg + ma\\Tension = Weight + ma$

Hence, the tension will increase by an amount equal to "ma".