A block of mass m=10 kg at rest slides down a rough incline plane of θ=30° and length l=5 m. The coefficient of kinetic friction between the block and the incline is μ_k=0.1. At the bottom of the plane the block continues to slide on a frictionless surface and hits a spring with spring constant k=100 N/m.

Question

contestada

Respuesta :

batolisis batolisis · Answer 1 · 2021-12-27T13:01:54+01:00

The speed of the block at point B = 6.36 m/s

Given data :

Mass ( m ) = 10 kg

Angle of inclination ( θ ) = 30°

Length of incline = 5 m

Determine the speed of the block at a point B on the incline

First step : Calculate the work done by frictional force

given that there is no friction on the horizontal plane. Vinclined = Vhorizontal

∴ Work done by frictional force ( Wf ) = F * L cos 180

= - ( μ_k * N ) L

= - (0.1 * 84.86 ) * 5 = - 42.4 Joule

where N = mg cos 30°

= 10 * 9.8 * 0.866 = 84.86

Next step : Calculate the speed of the block at point B

applying work energy theorem

Wf = ΔK.E + ΔP.E

= ( 1/2 mv² - 0 ) + ( 0 - mgh )

∴ - 42.48 = 1/2 mv² - mgh

1/2 mv² = mgh - 42.48

= 10 * 9.8 * 5 sin 30° - 42.4

v² = 40.52

V ( speed of the block at point B ) = 6.36 m/s

Hence we can conclude that the speed of the block at point B = 6.36 m/s

Learn more about speed on frictionless surface : https://brainly.com/question/9968388

Attached below is the complete question related to your question