Question

A child pulls a wagon across the grass so that it accelerates using a force of 50 N at an angle of 42 degrees above the ground. The loaded wagon has a mass of 12 kg. If the coefficient of friction between the wagon and grass is 0.64. What is the acceleration of the wagon? Describe the motion of the wagon.

Answer 1

Answer:

$-1.398\ \text{m/s}^2$

Decelerating or slowing down

Explanation:

F = Force = 50 N

$\theta$ = Angle force is being applied = $42^{\circ}$

$\mu$ = Coefficient of friction = 0.64

m = Mass of wagon = 12 kg

g = Acceleration due to gravity = $9.81\ \text{m/s}^2$

Normal force is given by

$N=mg-F\sin\theta$

Frictional force is given by

$f=\mu N\\\Rightarrow f=\mu (mg-F\sin\theta)$

The force balance is given by

$F\cos\theta-f=ma\\\Rightarrow \dfrac{F\cos\theta-\mu (mg-F\sin\theta)}{m}=a\\\Rightarrow a=\dfrac{50\times \cos42^{\circ}-0.64(12\times 9.81-50\times\sin42^{\circ})}{12}\\\Rightarrow a=-1.398\ \text{m/s}^2$

The acceleration of the wagon is $-1.398\ \text{m/s}^2$. The negative sign indicates that the wagon is decelerating or slowing down.