Question

a car of 1000kg moves up a hill inclined at 30degree to the horizontal.if the total frictional force is 100N.find the force if the car is accelerating at 2m/s

Answer 1

a car of $1000\mathrm{kg}$ moves up a hill inclined at 30degree to the horizontal. if the total frictional force is 100N.find the force if the car is accelerating at $2\mathrm{m / s}$

Solution:

$m = 1000kg - mass$ of the car;

$\alpha = 30{}^{\circ} - angle$ with the horizon;

$F_{f} = 100N - \text{total friction force};$

$a = 2\frac{m}{s^2} -$ acceleration of the car;

Newton's second law for the car:

$\vec{F}_f + \overline{m}\vec{g} +\vec{N} +\vec{F} = m\vec{a}$

$x:F - F_{f} - mg_{x} = ma$ (1)

From the right triangle ABC:

$\sin \alpha = \frac{mg_x}{mg} \Rightarrow mg_x = mg \sin \alpha$ (2)

(2)in(1):

$F - F_{f} - mg\sin \alpha = ma$

$F = ma + F_{f} + mg\sin \alpha = 1000kg\cdot 2\frac{m}{s^{2}} +100N + 1000kg\cdot 9.8\frac{N}{kg}\cdot \sin 30{}^{\circ}$

$= 7000N$

Answer: the force is $F = 7000N$ .