Two blocks, (mass ) and (mass )

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two blocks,

A

(mass

4.0\,\text{kg}

) and

B

(mass

6.0\,\text{kg}

), rest on a frictionless horizontal surface and are connected by a light, inextensible string. A horizontal force

\vec F_{\text{push}}

is applied to block

A

so that the entire system accelerates to the right. Engineers require the acceleration of the system to be

2.5\,\text{m}\,\text{s}^{-2}

, but the string can withstand a maximum tension of only

20\,\text{N}

before breaking. (a) In terms of

F_{\text{push}}

, state expressions for the net horizontal force on each block and for the tension

T

in the string. (b) Derive an equation relating

F_{\text{push}}

and

T

using Newton’s second law for one of the blocks. (c) Calculate the value of

F_{\text{push}}

that produces the target acceleration for the system. (d) Using your result from part (c), determine the resulting tension in the string and state quantitatively whether the engineering limit of

20\,\text{N}

is exceeded. (e) If the limit is exceeded, compute the maximum possible acceleration of the system that still keeps the tension within

20\,\text{N}

and explain your reasoning.

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