Answer:
Step-by-step explanation:
Consider first case with incline:
It is frictionless so the only force on mass is gravity, g.
The force has two components: one that is along the incline direction and another perpendicular to the incline.
The perpendicular component does no work as it is perpendicular to the direction of motion.
The incline component of gravity = g*sinθ
=10*sin30deg; using 10m/s^2 for g
Length of incline = 5/sinθ = 5/sin30deg
Work done = force * distance
= mass * acceleration * distance
= 5 * 10*sin30deg * 5/sin30deg
= 250J
Mass starts from rest so its initial speed=0
Using the kinematic equation: final speed^2 = initial speed^2 + 2*acceleration*distance
Final speed^2 = 0 + 2*(10*sin30deg)*(5/sin30deg)
= 2*10*5
=100
Final speed = 10m/s
Now for the second case of vertical drop:
Work done by gravity = mass * gravity * height
= 5 * 10 * 5
= 250J
Using conservation of energy, Final kinetic energy = Work done by gravity
1/2 * Mass * Final speed^2 = 250
Final speed^2 = 2 * 250 / 5 = 100
Final speed = 10m/s
In both scenarios, the work done by gravity and the mass' final speed are the same.