Question

a 20kg wagon is pulled along the level ground by a rope inclined at 30 degree above the horizontal.
A friction force of 30N opposes the motion. How large is the pulling force if the wagon is moving with (a) constant speed and (b) an acceleration of 0.40 m/s

Answer 1

a 20kg wagon is pulled along the level ground by a rope inclined at 30 degree above the horizontal. A friction force of 30N opposes the motion. How large is the pulling force if the wagon is moving with (a) constant speed and (b) an acceleration of $0.40 \, \text{m/s}$ .

$F_{fr}$ - friction force

$F$ - pulling force

a) Constant speed $\Rightarrow$ acceleration equals 0. Newton's first law of motion on $x$ -axis:

$$F \cos (3 0) = F _ {f r}$$ $$F = \frac {F _ {f r}}{\cos (3 0)} = \frac {3 0}{\sqrt {3}} 2 = 2 0 \sqrt {3} N$$

Answer: $F = 20\sqrt{3} N$

b) Newton's second law of motion:

$$m a = F \cos (3 0) - F _ {f r}$$ $$F = \frac {(m a + F _ {f r})}{\cos (3 0)} = \frac {2 0 + 0 . 4 + 3 0}{\sqrt {3}} 2 = \frac {7 6}{\sqrt {3}} N$$

Answer: $F = \frac{76}{\sqrt{3}} N$