Question

6.A car traveling at 20 m/s goes around an unbanked curve in the road which has a radius of 122 m. The acceleration experienced by the car is ___m/s2. (Give your answer with the correct number of significant digits and do not include units)

7.An object traveling in a circle with a radius of 5.0 m has a frequency of 6.0 Hz. The speed of the object is ___x102 m/s. (Give your answer with the correct number of significant digits and do not include units)

8.If the centripetal acceleration on a stone being whirled in a circle at the end of a 1.75 m string is 350 m/s2, the frequency of rotation is ___Hz? (Give your answer with the correct number of significant digits and do not include units)

9.A 1000 kg car enters an unbanked curve of 80 m radius. If the coefficient of friction between the pavement and the car tires is 0.51, the maximum speed which the car can go around the curve is ___m/s. (Give your answer with the correct number of significant digits and do not include units)

Answer 1

6)

$$a=\dfrac{v^2}{r}=\dfrac{(20\ \dfrac{m}{s})^2}{122\ m}=3.27\ \dfrac{m}{s^2}.$$

7) Let's first find the period of the rotation of the object:

$$T=\dfrac{1}{f}=\dfrac{1}{6.0\ Hz}=0.167\ s.$$

Finally, we can find the speed of the object:

$$v=\dfrac{2\pi r}{T}=\dfrac{2\pi\cdot5.0\ m}{0.167\ s}=1.88\cdot10^2\ \dfrac{m}{s}.$$

8) Let's first find the period of the stone's rotation:

$$F_c=ma_c,$$ $$ma_c=\dfrac{4\pi^2mr}{T^2},$$ $$T=\sqrt{\dfrac{4\pi^2r}{a_c}},$$ $$T=\sqrt{\dfrac{4\pi^2\cdot1.75\ m}{350\ \dfrac{m}{s^2}}}=0.444\ s.$$

Finally, we can find the frequency of rotation:

$$f=\dfrac{1}{T}=\dfrac{1}{0.444\ s}=2.25\ Hz.$$

9)

$$F_{c}=F_{fr},$$ $$\dfrac{mv^2}{r}=\mu mg,$$ $$v=\sqrt{\mu gr}=\sqrt{0.51\cdot9.8\ \dfrac{m}{s^2}\cdot80\ m}=20\ \dfrac{m}{s}.$$