AP Physics B & C – Two Multiple Choice Questions (for practice) on Newton’s Laws of Motion

"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."

– Albert Einstein

Two practice questions (MCQ) on Newton’s laws of motion are given below with solution. Even though these are meant for AP Physics C aspirants, they should not be difficult for those who are preparing for AP Physics B Exam.

(1) In the system shown in the adjoining figure, the horizontal surface on which block A is placed is smooth and the pulleys are light and frictionless. If g = 10 ms^–2, the tension T in the string (which may be assumed to be weightless and inextensible) is

(a) 1 N

(b) 2N

(c) 5 N

The velocity of the iron block at the moment of hitting the nail is 6 ms^–1.

(d) 10 N

(e) 20 N

Net force driving the system = Weight of B = mg = 2×10 = 20 N.

Acceleration (a) of the system is given by

a = Driving force /Total mass moved = ²⁰/₄ = 5 ms^–2.

Tension, T = Weight of B moving down (as in a lift) = m(g – a) = 2(10 – 5) =10 N.

(2) An iron block of mass 8 kg falling vertically down hits a nail on a block of wood (fig.). The velocity of the iron block at the moment of hitting the nail is 6 ms^–1. If the nail penetrates through 2 cm into the wooden block due to the impact, what is the force exerted by the iron block on the nail?

(a) 1600 N

(b) 2200 N

(c) 4800 N

(d) 7200 N

(e) 9600 N

The acceleration (in fact, retardation), a of the iron block during the impact is given by

0 = 6² + 2a×(0.02), from the equation v² = u² + 2as

This gives a = – 900 ms^–2

The negative sign shows that the iron block is retarded.

The retarding force exerted by the nail on the iron block is of magnitude F given by

F = ma = 8×900 = 7200 N

The force exerted by the iron block on the nail is equal and opposite to that exerted by the nail on the iron block. The answer therefore is 7200 N.

[The above question can be modified as follows:

An iron block of mass 8 kg falling freely from rest under gravity from a height of 1.8 m hits a nail on a block of wood (fig.). If the nail penetrates through 2 cm into the wooden block due to the impact, what is the force exerted by the iron block on the nail? (g = 10 ms^–2)

(a) 1600 N

(b) 2200 N

(c) 4800 N

(d) 7200 N

(e) 9600 N

The answer will be unchanged since the velocity at the moment of hitting the nail will be 6 ms^–1 itself (v = √(2gh) = √(2×10×1.8) = √(36) = 6)].