Friction in Curved Roads

Q.

A car has to move on a level turn of radius 90 m. If the coefficient of static friction between the tyre and the road is 1.0, find the maximum speed the car can take without skidding.

1. 10 m/s

2. 20 m/s

3. 30 m/s

4. 40 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. 30 m/s

2. 10 m/s

3. 40 m/s

4. 20 m/s

Q.

Consider a vehicle going on a horizontal road towards east. Neglect any force by the air. The frictional forces on the vehicle by the road

1. Is towards east if the vehicle is accelerating

2. Is zero if the vehicle is moving with a uniform velocity

3. Must be towards east

4. Must be towards west

Q. What should be the value of coefficient of static friction between the tyre and the road, when a car travelling at speed of $60km{h}^{-1}$ makes a level turn of radius $40\text{m}$?

1. $0.5$
2. $0.66$
3. $0.71$
4. $0.80$

Q. A car of mass $2000kg$ is moving with a constant speed of $10m{s}^{-1}$ on a circular path of radius $20\text{m}$ on a level road. What must be the frictional force between the car and the road so that the car does not slip on the road ?

1. ${10}^3\text{N}$
2. ${10}^5\text{N}$
3. ${10}^2\text{N}$
4. ${10}^4\text{N}$

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. $14.4km{h}^{-1}$
4. $21.6km{h}^{-1}$

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 $10m{s}^{-2}$, then maximum allowable speed for the car will be (in $km{h}^{-1})$

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

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 car is moving on a circular level road of radius $300\text{m}$. If the coefficient of static friction is $0.3$, maximum safe speed (in $\text{km/h}$) of the car can be

[Take $g=10{\text{m/s}}^2$]

Q. What should be the value of coefficient of static friction between the tyre and the road, when a car travelling at speed of $60km{h}^{-1}$ makes a level turn of radius $40\text{m}$?

1. $0.5$
2. $0.66$
3. $0.71$
4. $0.80$