"A 0.4 kg mass, attached to the end of a 0.75 m string, is whirled around in a circular horizontal path. If the maximum tension
that the string can withstand is 450 N, then what maximum velocity can the mass have if the string is not to break?"
2 answers:
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(a) 252 N, opposite to the applied force
There are two forces acting on the refrigerator in the horizontal direction:
- the pushing force of 252 N, F, forward
- the frictional force, Ff, pulling backward
In this case, the refrigerator is not moving: this means that its acceleration is zero. According to Newton's second law, this also means that the net force acting on the refrigerator is also zero:
So we have
which means that the frictional force is equal in magnitude to the pushing force:
and the direction is opposite to the pushing force.
(b) 334.8 N
The force that must be applied to the refrigerator to make it moving is equal to the maximum force of friction, which is given by:
where
is the coefficient of static friction
m = 56 kg is the mass of the refrigerator
g = 9.8 m/s^2 is the acceleration of gravity
Substituting:
F_max = (0.61)(56 kg)(9.8 m/s^2)=334.8 N