Question

Unless otherwise stated, all objects are located near the Earth's surface, where g = 9.80 m/s2 .A girl pushes a 20 kg lawn mower as shown in the figurea) If F = 27 N and θ = 36 ∘ what is the acceleration of the mower? Ignore friction. b) What is the normal force exerted on the mower by the lawn?

Answer 1

Before we begin we need to make the free body diagram of the situation, it is shown below:

Now, from Newton's second law we have that:

$\begin{gathered} F\cos \theta=ma \\ N-W+F\sin \theta=0 \end{gathered}$

a)

From the first equation we have that:

$\begin{gathered} a=\frac{F\cos \theta}{m} \\ a=\frac{27\cos 324}{20} \\ a=1.09 \end{gathered}$

Therefore the acceleration of the mower is 1.09 meters per second per second.

b)

From the second equation we have:

$\begin{gathered} N=W-F\sin \theta \\ N=(20)(9.8)-27\sin 324 \\ N=211.87 \end{gathered}$

Therefore the normal force is 211.87 N