Question

A rubber-wheeled 50 kg cart rolls down a 35 degree concrete incline. Coefficient of rolling friction between rubber and concrete is = 0.02. (a) What is the cart's acceleration if rolling friction is neglected? (b) What is the cart's acceleration if rolling friction is included?

Answer 1

(a) 5.62 m/s²

(b) 5.46 m/s²

Step-by-step explanation:

The given values are:

mass,

m = 50 kg

angle

= 35°

(a)

If friction neglected,

⇒
`F_x=mgSin \theta=ma`

⇒
`a_x=gSin \theta`

`=9.8 \ Sin35^(\circ)`

`=5.62 \ m/s^2`

(b)

If friction present,

⇒
`F_x=mgCos \theta`

⇒
`F_x=mgSin \theta-\mu_r mgCos \theta`

⇒
`a=gSin \theta-\mu_rgCos \theta`

`=9.8 \ Sin35^(\circ)-0.02* 9.8 \ Cos30^(\circ)`

`=5.46 \ m/s^2`