In a pickup game of dorm shuffleboard, students crazed by final exams use a broom to propel a calculus book along the dorm hallway. If the 3.5 kg book is pushed from rest through a distance of 0.78 m by the horizontal 26 N force from the broom and then has a speed of 1.68 m/s, what is the coefficient of kinetic friction between the book and floor?

Respuesta :

Answer:

μ=0.16

Explanation:

Given that

m= 3.5 Kg

d= 0.78 m

F= 26 N

v= 1.68 m/s

Lets take coefficient of kinetic friction = μ

Friction force Fr=μ m g

Lets take acceleration of block is a m/s²

F- Fr = m a

26 -  μ x 3.5 x 10 = 3.5 a         ( take g =10 m/s²)

a= 7.42 - 35μ  m/s²

The final speed of the block is v

v= 1.68 m/s

We know that

v²= u²+ 2 a d

u= 0 m/s given that

1.68² = 2 x a x 0.78

a= 1.80 m/s²

a= 7.42 - 35μ  m/s²

7.42 - 35μ = 1.80

μ=0.16

Answer:[tex]\mu =0.573[/tex]

Explanation:

Given

mass of book [tex]m =3.5 kg[/tex]

distance moved by book [tex]s=0.78 m[/tex]

Force applied [tex]F=26 N[/tex]

initial speed [tex]u=1.68 m/s[/tex]

coefficient of kinetic friction is [tex]\mu [/tex]

using [tex]v^2-u^2=2 as[/tex]

[tex]a=\frac{0-1.68^2}{2\times 0.78}[/tex]

[tex]a=1.809 m/s^2[/tex] deceleration

Net Force

[tex]F-f_r=ma[/tex]

[tex]F-ma=f_r[/tex]  , where [tex]f_r=friction\ force[/tex]

[tex]f_r=\mu N=\mu mg[/tex]

[tex]26-3.5\times 1.809=\mu \cdot 3.5\times 9.8[/tex]

[tex]\mu =\frac{26-6.33}{34.3}[/tex]

[tex]\mu =\frac{19.67}{34.3}=0.573[/tex]