Problem 1

A particle of mass

m

slides without friction from rest on a wedge of mass

M

and incline angle

\alpha

. The wedge rests on a smooth horizontal floor. Find the wedge's acceleration and the particle's acceleration relative to the wedge; gravity is

g

downward. (a) State the assumptions and establish the governing equation for the requested quantity. (b) Solve it in terms of the given symbols, identifying the direction, sign, or physical nature of the result. (c) Check a simple limiting case and state when the model remains valid. Use SI units consistently, retain the symbols in the setup, and enforce all geometric constraints and initial conditions.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

X=\text{tọa độ ngang của nêm},\quad s=\text{quãng đường hạt đi xuống dọc mặt nghiêng}

problems.proof.analysis

Take positive $s$ down the incline. The particle's horizontal coordinate is $x=X-s\cos\alpha$ , and its height decreases by $s\sin\alpha$ .