A 20-lb block slides down a 30° inclined plane with an initial velocity of 2 ft/s. Determine the velocity of the block in 3 s if the coefficient of kinetic friction between the block and the plane is μk = 0.25.

Question

A 20-lb block slides down a 30° inclined plane with an initial velocity of 2 ft/s. Determine the velocity of the block in 3 s if the coefficient of kinetic friction between the block and the plane is { \mu }_{ k } = 0.25.

Accepted Answer

[latex](+ warrow )\quad \quad m{ (v }_{ v' })+\Sigma \int _{ { t }_{ 1 } }^{ { t }_{ 2 } }{ { F }_{ { y }' }dt } =m{ (v }_{ y' })_{ 2 }\ 0+N(3)-20\cos { { 30 }^{ \circ }(3) } =0\quad \quad N=17.32lb\ (+\swarrow )\quad \quad m{ (v }_{ x' })_{ 1 }+\Sigma \int _{ { t }_{ 1 } }^{ { t }_{ 2 } }{ { F }_{ { x' } }dt } =m{ (v }_{ x' })_{ 2 }\ \frac { 20 }{ 32.2 } \left( 2 ight) +20\sin { { 30 }^{ \circ } } (3)-0.25(17.32)(3)=\frac { 20 }{ 32.2 } v\ v=29.4ft/s[/latex]

Question : A 20-lb block slides down a 30° inclined plane with an initi...