Question

A 19 kg rock slides on a rough horizontal surface at 9.25 m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is 0.63. What average thermal power (in Watts) is produced as the rock stops?

Answer 1

541.89 Watt

Step-by-step explanation:

Consider the motion of rock on rough surface

μ = Coefficient of kinetic friction = 0.63

acceleration caused to kinetic friction is given as

a = - μg

a = - (0.63) (9.8)

a = - 6.2 m/s²

v₀ = initial velocity of the rock = 9.25 m/s

t = time taken to stop

v = final velocity = 0 m/s

Using the equation

v = v₀ + a t

0 = 9.25 + (- 6.2) t

t = 1.5 sec

m = mass of the rock = 19 kg

Energy lost due to friction is given as

E = (0.5) m (v₀² - v²)

E = (0.5) (19) (9.25² - 0²)

E = 812.84 J

Average thermal power is given as

`P = (E)/(t)`

`P = (812.84)/(1.5)`

P = 541.89 Watt