A block of mass is placed on a smooth horizontal table

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A block of mass

m

is placed on a smooth horizontal table. Two mutually perpendicular horizontal forces

\vec{F}_1

and

\vec{F}_2

of magnitudes

F_1

and

F_2

act on the block simultaneously. (i) Show that the magnitude of the resultant force on the block is

\sqrt{F_1^{2}+F_2^{2}}

. (ii) Derive an expression for the magnitude of the acceleration of the block in terms of

F_1

F_2

and

m

. (iii) The mass of the block is now reduced to

\dfrac{m}{2}

while

F_1

and

F_2

remain unchanged. By what factor does the magnitude of acceleration change? Justify your answer. (iv) Determine a relation between new forces

F_1'

and

F_2'

and the new mass

m'

such that the acceleration of the block remains equal to the value obtained in part (ii).