If the toboggan accelerates very fast, the radio will slip relative to the toboggan (like pulling a tablecloth from under plates - the plates stay behind if the table-cloth's acceleration is big enough).
Think of the radio separately:
Weight: W = mg
Normal reaction: Fn = W = mg
Limiting frictional force = μFn = μmg
The radio's horizontal acceleration is caused by the horizontal frictional force (as this is the only horizontal force on the radio).
The maximum frictional force that can act on the radio is the limiting frictional force, μmg. This produces an acceleration (using F = ma):
a = F/m = μmg/m = μg = 0.450*9.81 = 4.4145m/s²
The system's total mass M = 6.16+3.08 = 9.24kg
The maximum acceleration is produced by the maximum tension T. Since T is the only external horizontal force on the system:
T = Ma = 9.24*4.4145 = 40.8N
A straight horizontal rope is towing a 6.13 kg toboggan across frictionless ice. A 3.06 kg radio is on top of the toboggan with a coefficient of static friction of 2.07 between the toboggan and radio. In order to prevent the radio from slipping, what is the largest force of tension for the rope
2 answers
how did you get the 0.450 ?