Question

a 2kg block of wood starts at rest and slides down a ramp. Its initail height is 12m. if the final velocity of the block is 13m/s, determine the energy of this system that has been turned into heat

Answer 1

E = 66.44 J

Step-by-step explanation:

From the law of conservation of energy:

Total Mechanical Energy at Start = Total Mechanical Energy at the End

Potential Energy at Start = Kinetic Energy at End + Energy Lost

`mgh = (1)/(2) mv^2 + E\\\\E = mgh - (1)/(2) mv^2\\\\`

where,

E = Energy turned into heat = ?

m = mass of block = 2 kg

g = acceleration due to gravity = 9.81 m/s²

h = height = 12 m

v = final speed = 13 m/s

Therefore,

`E = (2\ kg)(9.81\ m/s^2)(12\ m)-(1)/(2) (2\ kg)(13\ m/s)^2\\\\E = 235.44\ J - 169\ J\\`

E = 66.44 J