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# physics maximum force before string breaks?

Two masses m1 = 5.25 kg and m2 = 7.75 kg are connected by a light string, which has a breaking strength of

50.0 N. The masses are moving on a surface with a coefficient of kinetic friction of 0.600. A horizontal

force F is applied to m1 as shown.

Determine the maximum force F that can be applied without breaking the string between masses m1 and

m2.

Help walking me through this would be appreciated :)

### 2 Answers

- NCSLv 71 month agoFavorite Answer
First, apply Newton's Second to m₂:

m₂*a = T - µ*m₂*g → where T is the maximum tension

and µ*m₂*g is the friction force.

7.75 kg * a = 50.0N - 0.600 * 7.75kg * 9.81m/s²

solves to a = 0.5656

so that's the maximum allowable system acceleration.

Now apply N2 to m₁:

m₁*a = F - T - µ*m₁*g

5.25kg * 0.5656m/s² = F - 50.0N - 0.600 * 5.25kg * 9.81m/s²

solves to max F = 83.9 N

Hope this helps!