A model train with a mass of #2 kg# is moving along a track at #6 (cm)/s#. If the curvature of the track changes from a radius of #3 cm# to #8 cm#, by how much must the centripetal force applied by the tracks change?
2 Answers
The centripetal force changes by
Explanation:
The centripetal force is
The mass,
The speed,
The radius,
The variation in centripetal force is
The centripetal force is decreased by
Explanation:
The centripetal force is given in accordance with Newton's second law as:
#F_c=ma_c# where
#m# is the mass of the object and#a_c# is the centripetal acceleration experienced by the object
The centripetal acceleration can be expressed in terms of velocity as:
#a_c=(v^2)/r#
Therefore, we can state:
#F_c=(mv^2)/r#
The angular velocity can also be expressed in terms of the frequency of the motion as:
To find the change in centripetal force as the radius changes, we're being asked for
#DeltaF_c=(F_c)_f(F_c)_i#
#=(mv^2)/r_f(mv^2)/r_i#
We can simplify this equation:
#=>color(purple)(DeltaF_c=mv^2(1/r_f1/r_i))#
We are provided with the following information:

#>"m=2"kg"# 
#>v=0.06"m"//"s"# 
#>"r_i"=0.03"m"# 
#>"r_f"=0.08"m"#
Substituting these values into the equation we derived above:
#DeltaF_c=(2"kg")(0.06"m"//"s")^2(1/0.081/0.03)#
#=>color(crimson)(0.15"N")#
Therefore, the centripetal force is decreased by