Question

A 75 kg painter climbs a ladder that is 2.75 m long and leans against a vertical wall at an angle of 30º with the wall.
a) How much work does gravity do on the painter?
b) Does the answer to part (a) depend on whether the painter climbs at constant speed of accelerates up the ladder? Explain.

Answer 1

Answer:

1752.188625 Joules

No.

Explanation:

l = Length of ladder = 2.75 m

$\theta$ = Angle = 30°

m = Mass of person = 75 kg

g = Acceleration due to gravity = 9.81 m/s²

The height of the man from the ground at the top of the ladder is

$h=lcos30\\\Rightarrow h=2.75\times cos30=2.3815\ m$

Work done against gravity is given by

$P=mgh\\\Rightarrow P=75\times 9.81\times 2.3815\\\Rightarrow P=1752.188625\ J$

The work gravity does on the painter is 1752.188625 Joules

No, only the perpendicular height of the person is needed to find the work done against gravity. So, the speed or acceleration does not matter.