A child leaves her bag on a slide. The bag, which is at the top of the slide, st

Question

A child leaves her bag on a slide. The bag, which is at the top of the slide, starts from rest and reaches the bottom in 1.57s. The mass of the book bag is 3.95kg, the length of the slide is 3.50m and the angle of incline is 33.5 degrees. (Assume the +x-axis to be parallel to and down the slide. For all values, enter the magnitude only.)

a) With what acceleration does the bag go down the slide?

b) What is the friction force acting on the bag?

c) What is the coefficient of kinetic friction between the bag and the slide?

d) What is the speed of the bag when it reaches the bottom of the slide?

Explanation / Answer

here,

time taken to reach the bottom , t = 1.57 s

mass of the bag , m = 3.95 kg

theta = 33.5 degree

length of slide , l = 3.5 m

(a)

the accleration does the bag do down be a

using seccond equation of motion

l = u*t + 0.5*a*t^2

3.5 = 0 + 0.5 * a*1.57^2

a = 2.84 m/s^2

the acceleration does the bag go down the slide is 2.84 m/s^2

(b)

the deaccelration due to the friction force , d = g*sin(theta) - a

d = 2.57 m/s^2

frictional force , ff = m*d

ff = 10.15 N

the friction force acting on the bag is 10.15 N

(c)

let the coefficient of kinetic friction between the bag and the slide be u

u*m*g*cos(theta) = ff

u*3.95*9.8*cos(33.5) = 10.15

u = 0.31

the coefficient of kinetic friction between the bag and the slide is 0.31

(d)

let the speed of the bag when it reaches the bottom of the slide be v

v = v0 + a*t

v= 0 + 2.84*1.57

v = 4.46 m/s

the speed of the bag when it reaches the bottom of the slide is 4.46 m/s

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