Answer
(a) $51J, 51J$
(b) increase
Work Step by Step
(a) The work done by gravity along path 1 is:
$W_1=mgd_1cos\theta+mgd_2cos\theta$
We plug in the known values to obtain:
$W_1=(5.2)(9.81)(5.0)cos90^{\circ}+(5.2)(9.81)(1.0)cos0^{\circ}$
$\implies W_1=0+(5.2)(9.81)(1.0)(1)$
$W_1=51J$
The work done by gravity along path 2 is:
$W_2=mgd_1cos\theta+mgd_2cos\theta$
We plug in the known values to obtain:
$W_2=(5.2)(9.81)(1.0)cos0^{\circ}+(5.2)(9.81)(5.0)cos90^{\circ}$
$\implies W_2=(5.2)(9.81)(1.0)(1)+0$
$W_2=51J$
(b) We know that gravity is directly proportional to the mass of the object. Thus when the mass is increased, the gravity will also increase. As a result, the work done by the gravity will increase as well.
