Question

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (g=10ms^-2).

• A. 150 ms^-2
• B. 1.5 ms^-2
• C. 50 ms^-2
• D. 1.2 ms^-2

Answer 1

The Correct Option is B

To calculate the maximum acceleration of a moving car so that a body lying on the floor remains stationary, we start with the equation for static friction:

f_s = μ_s × N

where:

• f_s is the static frictional force.
• μ_s is the coefficient of static friction (given as 0.15).
• N is the normal force.

For an object on a flat surface, the normal force (N) is equal to the gravitational force, which is:

N = m × g

Here g is the acceleration due to gravity (10 m/s²), and m is the mass of the body. The maximum static frictional force (f_s,max) that can act on the body is:

f_s,max = μ_s × m × g

This static frictional force is what allows the body to remain stationary when the car accelerates. Therefore, the maximum static frictional force equals the maximum force due to acceleration that can be applied to the body:

f_s,max = m × a_max

Setting the two equations for f_s,max equal gives:

μ_s × m × g = m × a_max

Cancelling m from both sides (assuming it is non-zero):

μ_s × g = a_max

Substitute the given values to find a_max:

a_max = 0.15 × 10 = 1.5 m/s²

Therefore, the maximum acceleration of the car for the body to remain stationary is 1.5 m/s².

Answer 2

The correct option is (B): 1.5 ms^-2

\(F_s=ma\)

\(f_L=ma_{max}\)

\(\mu\,mg=ma_{max}\)

\(a_{max}=\mu g\)

\(=0.15(10)\)

\(=1.5\,m/s^2\)