Question

. A block slides down a ramp that has a length of 11.4 m. The block travels at a speed of 5.43 m/s at the bottom of the ramp and increased in temperature from 22.1°C to 22.3°C. The block is made of copper and has a specific heat capacity of 385 J/kg°C. What is the angle of the ramp?

Answer 1

$m\vec{g}+\vec{N}+\vec {F_{fr}}=m\vec a,$

$ma=mgsin\alpha-\mu mg cos\alpha,$

$\mu=\frac{gsin\alpha-a}{gcos\alpha},$

$v=at,~l=\frac{at^2}{2}\implies a=\frac{v^2}{2l},$

$A_{fr}=Q,$

$\mu mg\cos \alpha l=cm\Delta t,$

$(gsin\alpha-\frac{v^2}{2l})l=c\Delta t,$

$sin\alpha=\frac{v^2+2c\Delta t}{2gl}=0.82,$

$\alpha=55° .$