3. A four-wheeled minibus breaks down on a horizontal straight tarmac road. Given that its mass is 4000kg and the coefficient of static friction between the tyre, rubber and the tarmac is 0.7, determine how much force is applied by the passengers to just make it start moving.

Answer 1

To determine the force applied by the passengers required to just make the minibus start moving, we can use the concept of static friction.

The maximum static frictional force (\( F_s \)) that can be exerted before the minibus starts moving is given by the formula:

\[ F_s = \mu_s \times N \]

where:

• \( \mu_s \) is the coefficient of static friction,
• \( N \) is the normal force acting on the minibus.

Since the minibus is on a horizontal road, the normal force (\( N \)) is equal to the weight of the minibus, which is calculated as:

\[ N = m \times g \]

where:

• \( m \) is the mass of the minibus (4000 kg),
• \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)).

Now, we can calculate the normal force:

\[ N = 4000 , \text{kg} \times 9.81 , \text{m/s}^2 = 39240 , \text{N} \]

Next, we substitute this value into the frictional force equation:

\[ F_s = \mu_s \times N = 0.7 \times 39240 , \text{N} \]

Calculating this gives:

\[ F_s = 0.7 \times 39240 \approx 27468 , \text{N} \]

Therefore, the force applied by the passengers to just make the minibus start moving is approximately 27468 N.