Finding an expression for the maximum tension?

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SUMMARY

The discussion focuses on deriving an expression for the maximum tension (T) in a system where a toy cart of mass m1 is pulled with a block of mass m2 on top, subject to static friction (μ) and an incline angle (θ). The maximum tension is determined by balancing forces acting on the block, including gravitational force and frictional force. The final expression for maximum tension can be formulated as T = (m2 * g * sin(θ)) + (μ * m2 * g * cos(θ)), ensuring that the block does not slide off the cart.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of static friction and its coefficient (μ)
  • Familiarity with free-body diagrams
  • Basic trigonometry, particularly related to angles and forces
NEXT STEPS
  • Study the derivation of forces in inclined planes
  • Learn about static friction and its role in preventing motion
  • Explore advanced applications of free-body diagrams in physics problems
  • Investigate the effects of varying angles (θ) on tension and friction
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in mechanics, particularly those studying forces on inclined planes and frictional interactions.

JadeLove
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A toy cart of mass m1 moves on frictionless wheels as it is pulled by a string under tension T. A block of mass m2 rests on top of that cart. The coefficient of static friction between the cart and block is μ. Find an expression for the maximum tension T that will not cause the block to slide on the cart if the cart is rolled up of angle Ɵ above the horizontal. The string is parallel to the surface on which the cart rolls.

The reason I'm so confused is because I've been given a problem to solve without ANY variables, where do I even start?

I drew a free-body diagram but it doesn't really help... And theoretically, what is my answer supposed to even turn out to be, T = 0? T =1? I mean is the question asking me to work out a process where I get one of those answers :S Help!
 
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Variables that you've been given: m1, m2, T, μ, θ. You can assume that g is there, too; It's generally assumed.

It is fine to provide an answer that is a formula; there need not be a particular numerical answer.
 

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