A tractor with a mass of 1600 kg develops a maximum tractive effort of 3000 N in top gear on a concrete surface. The total rolling resistance is 160 N. If the gradient angle is defined as the angle that the inclined plane makes with the horizontal, the maximum gradient can be negotiated by the tractor is _________

a) 10.44°
b) 11.63°
c) 29.4°
d) 34.29°

Answer: a
Explanation:

Referring to figure
In the limiting case:
3000 = m_tg sin θ + 160
m_tg sin θ = 3000-160
m_tg sin θ = 2840
sin θ = \(\frac{2840}{mtg}=\frac{2840}{1600*9.8} \)
sin θ = 0.18112
θ = sin^-1(0.18112)
θ = 10.44°.