Physics · Laws Of Motion · NEET
The forward force on the object is friction, which has a maximum value f_max = μs·N = μs·m·g. This friction must supply the whole force needed to accelerate the object: m·a = f. So m·a_max = μs·m·g, and the mass m cancels from both sides, leaving a_max = μs·g. This is why in NEET numericals the mass of the body (like 15 kg) is a distractor and is never used.
When the car floor accelerates forward, static friction between the object and the floor is the only horizontal force on the object. Friction acts forward (in the direction of the car's motion) to carry the object along with the car. If the car needs more force than friction can give, the object cannot keep up and slides backward relative to the floor.
Use static friction (μs). As long as the object does NOT slide, it moves together with the car, so there is no relative sliding, which means static friction. The largest acceleration the static friction can support is a_max = μs·g. Kinetic friction only starts once the object has already begun to slide.
If the car's acceleration is greater than μs·g, friction cannot supply enough force to accelerate the object at the same rate. The object then slides backward relative to the car floor, and kinetic friction takes over. The threshold value a_max = μs·g is exactly the point where the object is about to slip.
It slides backward relative to the car (toward the rear). The car floor rushes ahead faster than friction can carry the object, so from inside the car the object appears to move backward. In an accelerating (non-inertial) frame this is explained by a backward pseudo force, which the next concept covers.
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 = 10 m/s²):
A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12. Keeping the box stationary relative to the trolley, the maximum horizontal acceleration with which the trolley can be moved is (g = 10 m/s²):
Try the real previous-year questions from this chapter — each with the answer and a full solution.
a_max = μs·g, where μs is the coefficient of static friction between the object and the floor and g = 10 m/s².
Because friction (μs·m·g) provides the accelerating force (m·a). The mass m appears on both sides and cancels, so the answer only depends on μs and g.
Static friction, because the object is not yet sliding. The maximum static friction sets the limit a_max = μs·g.
The object slides backward relative to the car and kinetic friction acts. a_max = μs·g is the just-about-to-slip value.
It is a direct one-step formula question (2023 and 2026 papers) where the mass is a trap. Knowing a_max = μs·g gives a quick, sure mark.
