Question

a rope is used to pull a skier up a 10 degree slope, if the coefficient of kinetic friction is 0.18 and the mass of the skier is 80KG what is the Tension of the rope if the skier is accelerating at 0.5m.s ^-2

Answer 1

Answer on Question 78111, Physics, Mechanics, Relativity

Question:

A rope is used to pull a skier up a 10-degree slope. If the coefficient of kinetic friction is 0.18 and the mass of the skier is $80 \, kg$ what is the tension of the rope if the skier is accelerating at $0.5 \, m/s^2$ ?

Solution:

Let's apply the Newton's Second Law of Motion in projections on axis $x$ and $y$ :

$$\sum F _ {x} = m a _ {x},$$ $$T - m g \sin \theta - F _ {f r} = m a,$$ $$\sum F _ {y} = m a _ {y} = 0,$$ $$N - m g c o s \theta = 0,$$ $$N = m g c o s \theta .$$

Since, $F_{fr} = \mu_k N$ , we can write:

$$T - m g \sin \theta - \mu_ {k} m g \cos \theta = m a.$$

From this equation we can find the tension in the rope:

$$\begin{array}{l} T = m g \sin \theta + \mu_ {k} m g \cos \theta + m a = \\ = 8 0 k g \cdot 9. 8 \frac {m}{s ^ {2}} \cdot \sin 1 0 {}^ {\circ} + 0. 1 8 \cdot 8 0 k g \cdot 9. 8 \frac {m}{s ^ {2}} \cdot \cos 1 0 {}^ {\circ} + 8 0 k g \\ \cdot 0. 5 \frac {m}{s ^ {2}} = 3 1 5 N. \\ \end{array}$$

Answer:

$$T = 3 1 5 N.$$

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