A particle is projected with an initial speed of 4.6 m/s along a surface for whi

Question

A particle is projected with an initial speed of 4.6 m/s along a surface for which the coefficient of kinetic friction is 0.7. Find the distance it travels given that: A) the surface is horizontal B) the particle moves up a 24degree incline C) the particle moves down a 24degree incline A particle is projected with an initial speed of 4.6 m/s along a surface for which the coefficient of kinetic friction is 0.7. Find the distance it travels given that: A) the surface is horizontal B) the particle moves up a 24degree incline C) the particle moves down a 24degree incline A) the surface is horizontal B) the particle moves up a 24degree incline C) the particle moves down a 24degree incline

Explanation / Answer

here,

initial speed , u = 4.6 m/s

uk = 0.7

a)

when the surface is horizontal

the distance travelled be s

accelration , a = net force /effective mass

a = - uk * m * g /m = - 6.867 m/s^2

s = - u^2 /2a

s = 4.6^2 /( 2 * 6.867) = 1.54 m

b)

when the particle moves up a 24degree incline

the distance travelled be s

accelration , a = net force /effective mass

a = - (uk * m * g * cos(theta) + m * g * sin(theta))/m

a = - ( 0.7 * 9.81 * cos(24) + 9.81 * sin(24))

a = - 10.26 m/s^2

s = - u^2 /2a

s = 4.6^2 /( 2 * 10.26) = 1.03 m

c)

when the particle moves down a 24 degree incline

the distance travelled be s

accelration , a = net force /effective mass

a = - (uk * m * g * cos(theta) - m * g * sin(theta))/m

a = - ( 0.7 * 9.81 * cos(24) - 9.81 * sin(24))

a = - 2.28 m/s^2

s = - u^2 /2a

s = 4.6^2 /( 2 * 2.28) = 4.64 m

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