Friction in Curved Roads

Q. A circular road course track has a radius of $500\text{m}$ and is banked to ${10}^{\circ }$. If the coefficient of friction between the road and tyre is $0.25$, compute (i) the maximum speed to avoid slipping (ii) optimum speed to avoid wear and tear of the tyres. [Take $\tan {10}^{\circ }=0.1763$]

1. $46.74\text{m/s}$, $29.39\text{m/s}$
2. $30\text{m/s}$, $24\text{m/s}$
3. $74.46\text{m/s}$, $23.39\text{m/s}$
4. $50\text{m/s}$, $44\text{m/s}$

Q.

A 1500-kg car moving o a flat, horizontal road negotiates a curve as show in figure. If the radius of the curve is 20.0 m and the coefficient of static friction between the tires and dry pavement is 0.50, find the maximum speed the car can have and still make the turn successfully.

1. 20 m/s

2. 10 m/s

3. 30 m/s

4. 40 m/s

Q. The rear side of a truck is open and a box of $40kg$ mass is placed $5m$ away from the open end as shown in figure. The coefficient of friction between the box and the surface below it is $0.15$. On a straight road, the truck starts from rest and accelerates with $2m{s}^{-2}$. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

Q. A car is negotiating a curve of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between tyres and road is $\mu$. The maximum safe velocity is

1. $\sqrt{gR\left[\frac{\mu +\tan \theta }{1-\mu \tan \theta }\right]}$
2. $\sqrt{\frac{g}{R^2}\left[\frac{\mu +\tan \theta }{1-\mu \tan \theta }\right]}$
3. $\sqrt{\frac{g}{R}\left[\frac{\mu +\tan \theta }{1-\mu \tan \theta }\right]}$
4. $\sqrt{g{R}^2\left[\frac{\mu +\tan \theta }{1-\mu \tan \theta }\right]}$

Q. A $1500kg$ car moving on a flat road negotiates a curve whose radius is $35m$. If the coefficient of static friction between the tyres and the dry pavement is $0.5$. Find the maximum speed, the car can have in order to make the turn successfully.

1. $13.1m/s$
2. $20m/s$
3. $25m/s$
4. $15.1m/s$

Q. What should be the maximum speed with which a car can be driven through a curve of radius $18m$ without skidding (where, $g=10m{s}^{-2}$, coefficient of static friction between the rubber tyres and the roadway is $0.2$)?

1. $36.0km{h}^{-1}$
2. $18.0km{h}^{-1}$
3. $21.6km{h}^{-1}$
4. $14.4km{h}^{-1}$

Q.

A track consists of two circular parts ABC and CDE of equal radius 100 m and joined smoothly as shown in figure. Each part subtends a right angle at its centre. A cycle weighing 100 kg together with the rider travels at a constant speed of 18 km/hr on the track. What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed? Take g = 10 m/s²

1. 

2. 

3. 1.037

4. 0.732

Q. A circular road course track has a radius of $500\text{m}$ and is banked to ${10}^{\circ }$. If the coefficient of friction between the road and tyre is $0.25$, compute (i) the maximum speed to avoid slipping (ii) optimum speed to avoid wear and tear of the tyres. [Take $\tan {10}^{\circ }=0.1763$]

1. $46.74\text{m/s}$, $29.39\text{m/s}$
2. $30\text{m/s}$, $24\text{m/s}$
3. $74.46\text{m/s}$, $23.39\text{m/s}$
4. $50\text{m/s}$, $44\text{m/s}$

Q. Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with $1m{s}^{-2}$. What is the net force on the man? If the coefficient of static friction between the man's shoes and the belt is $0.2$, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man $=65kg$)

Q.

A block of mass $15kg$ is placed on a long trolley. The coefficient of static friction between the block and the trolley is $0.18$. The trolley accelerates from rest with $0.5m{s}^{-2}$ for $20s$ and then moves with uniform velocity. Discuss the motion of the block as viewed by,

Q. A car is moving on a levelled circular road of radius of curvature $300\text{m}$. If the coefficient of static friction is $0.3$ and acceleration due to gravity is $10{\text{ms}}^{-2}$, then maximum allowable speed for the car will be (in ${\text{kmh}}^{-1})$

1. $108$
2. $30$
3. $162$
4. $81$