Topic: Dynamics
Concepts: Statics

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Solution:

To keep the rope from slipping, the friction force must balance the weight of Becky:

Since for static friction $f \leq \mu_s N$,

so this is the minimum normal force Jonathan needs to exert. Therefore, the answer is E.

Topic: Energy
Concepts: Energy dissipation

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Solution:

From the previous problem, Jonathan applies a normal force $N=Mg/\mu_s$. After Becky makes a small jump, friction becomes kinetic since the rope starts slipping. The energy dissipated as Becky slides down is

Becky’s initial gravitational potential energy is converted to kinetic energy as she falls. Conserving energy, we have

so the answer is D.