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Chapter 12: Q57P (page 351)

In Fig 12-66, asphere is supported on a frictionless plane inclined at angle θ=45°from the horizontal. Angle ϕis 25°. Calculate the tension in the cable.

Short Answer

Expert verified

Tension in the cable is76 N.

Step by step solution

01

Listing the given quantities

θ=45°

ϕ=25°

Mass of spherem=10 kg

02

Understanding the concept of force and tension

We draw the free body diagram for the sphere. From this, we take the summation of all forces in the direction parallel to the ramp. After solving the equation, we will get the tension in the cable.

Equation:

∑Fx=0

03

Free Body Diagram

04

Calculation of tension in the cable

∑Falongtheinclinedplane=0(Tcosϕ)−(mgsinθ)=0(Tcosϕ)=(mgsinθ)T=(mgsinθ)cosϕT=10 kg×9.8 m/s2×sin45°cos25°T=76 N

Tension in the cable is76 N

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