Friction and Horizontal Circular Motion Problems

Q.

In death well (a motorcyclist drives the motorcycle on a vertical wooden well, you may have seen this act in circus), which force provides the necessary centripetal force?

Q. A $1200\text{kg}$ automobile rounds a level curve of radius $200\text{m}$, on an unbanked road with a velocity of $72\text{km/h}$. What is the minimum coefficient of static friction between the tyres and road in order that the automobile may not skid? $(g=10{\text{m/s}}^2)$

1. $0.15$
2. $0.2$
3. $0.3$
4. $0.4$

Q. A stunt driver of mass $60\text{kg}$ rides a bike inside a hollow metallic sphere of radius $45\text{m}$. Assume the bike moves in the central plane of the sphere. If the coefficient of static friction between the wheels of the bike and the metal surface is $0.8$, what must be the minimum speed of the driver so that he does not crash? Take $g=10{\text{m/s}}^2$.

1. $23.72\text{m/s}$
2. $40\text{m/s}$
3. $25.72\text{m/s}$
4. $50\text{m/s}$

Q. A car travels at a constant speed of $30\text{m/s}$ around a level circular bend of radius $100\text{m}$. What is the minimum coefficient of static friction between the tires and the road in order for the car to go round the bend without skidding?

1. $0.8$
2. $0.9$
3. $0.7$
4. $0.55$

Q. A car of mass $800\text{kg}$ moves on a horizontal circular track of radius $40\text{m}$. If the coefficient of static friction (${\mu }_s$) is $0.5$, then the maximum velocity with which the car can move will be

1. $15\text{m/s}$
2. $20\text{m/s}$
3. $25\text{m/s}$
4. $14\text{m/s}$

Q. A turn of radius $20\text{m}$ is banked for the vehicle of mass $200\text{kg}$ going at a speed of $10\text{m/s}$. The minimum coefficient of static friction required, if the vehicle moves with a speed of $15\text{m/s}$ is given by $\frac{n}{8}$. Then, $n$ is
[Take $g=10{\text{m/s}}^2$]

Q.

A particle of mass m rotates with a uniform angular speed $\omega$. It is viewed from a frame rotating about the Z-axis at a distance a from the particle, with a uniform angular speed ${\omega }_0$. The centrifugal force on the particle is

1. m${\omega }^2$a

2. m${\omega }_0^2$a

3. m ${\left(\frac{\omega +{\omega }_0}{2}\right)}^2$ a

4. m $\omega {\omega }_{0}a$

Q. A car of mass $800\text{kg}$ moves on a horizontal circular track of radius $40\text{m}$. If the coefficient of static friction (${\mu }_s$) is $0.5$, then the maximum velocity with which the car can move will be

1. $15\text{m/s}$
2. $20\text{m/s}$
3. $25\text{m/s}$
4. $14\text{m/s}$