Question

A car of mass 1000kg negotiates a banked curve of radius 90 m on a fictionless road. If the banking angle is 45degree, the speed of car is
(1) 5m/sec
(2)10m/sec
(3)20m/sec
(4)30m/sec

Answer 1

Answer on Question #46893-Physics-Mechanics-Kinematics-Dynamics

A car of mass $1000\mathrm{kg}$ negotiates a banked curve of radius $90\mathrm{m}$ on a fictionless road. If the banking angle is 45 degree, the speed of car is

(1) $5\mathrm{m / sec}$

(2) $10 \mathrm{~m} / \mathrm{sec}$

(3) $20 \mathrm{~m} / \mathrm{sec}$

(4) $30 \mathrm{~m} / \mathrm{sec}$

Solution

Radius of curve is $r = 90 \, \text{m}$ .

Banking angle is $\theta = 45{}^{\circ}$

Free-fall acceleration is $g = 10\frac{m}{s^2}$ .

No friction speed is .

From the free-body diagram for the car:

$$F _ {n e t} = F _ {c e n t r i p e t a l}.$$ $$m g \tan \theta = \frac {m v ^ {2}}{r}.$$ $$v = \sqrt {r g \tan \theta} = \sqrt {9 0 \cdot 1 0 \tan 4 5} = 3 0 \frac {m}{s}.$$

Answer: (4) $30\frac{m}{s}$ .

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