Question

Answer the following problem. Show your solution

1.A stone which has a mass of 1.27 kg is tied to a rope of 9 m and moved in a circular motion. If it is moving at the rate of 5 m/s. What is the cantripetal force acting on it?

2.A 1500kg truck, running at a speed of 10.5 m/s and rounding a curve with a curvature 200m.Find it's centripetal force.

3. What is the centripetal force of an 9000-7kg train, running at a speed of 27.8 m/s and rounding a curve with a curvature radius of 150 m?

Answer 1

1)

$$F_c=ma_c=\dfrac{mv^2}{r},$$ $$F_c=\dfrac{1.27\ kg\cdot(5\ \dfrac{m}{s})^2}{9\ m}=3.53\ N.$$

2)

$$F_c=ma_c=\dfrac{mv^2}{r},$$ $$F_c=\dfrac{1500\ kg\cdot(10.5\ \dfrac{m}{s})^2}{200\ m}=827\ N.$$

3)

$$F_c=ma_c=\dfrac{mv^2}{r},$$ $$F_c=\dfrac{9000\ kg\cdot(27.8\ \dfrac{m}{s})^2}{150\ m}=4.64\cdot10^4\ N.$$