The force F⃗ in Fig. 12-70 keeps the 6.40 kg block and the pulleys in equilibrium. The pulleys h

step 1 In this problem on the topic of equilibrium and elasticity, we are shown a 6 .4 KG block in the

The force F⃗ in Fig. 12-70 keeps the 6.40 kg block and the...

The force $\vec{F}$ in Fig. $12-70$ keeps the 6.40 $\mathrm{kg}$ block and the pulleys in equilibrium. The pulleys have negligible mass and friction. Calculate the tension $T$ in the upper cable. (Hint: When a cable wraps halfway around a pulley as here, the magnitude of its net force on the pulley is twice the tension in the cable.)

The force $\vec{F}$ in Fig. $12-70$
keeps the 6.40 $\mathrm{kg}$ block and the pulleys in
equilibrium. The pulleys have negligible
mass and friction. Calculate the tension $T$ in
the upper cable. (Hint: When a cable wraps
halfway around a pulley as here, the
magnitude of its net force on the pulley is twice
the tension in the cable.)

Key Concepts

Static Equilibrium

Static equilibrium refers to a state where an object is at rest, and the sum of all forces and torques acting on it is zero. This principle is crucial in analyzing systems where various forces, including gravitational, tension, and applied forces, balance each other to keep the system in a state of rest.

Tension in Cables

Tension is the pulling force transmitted along a rope, string, or cable when it is pulled tight by forces acting from opposite ends. In problems involving ideal (massless and frictionless) cables, the tension is constant throughout the length of the cable, making it a key concept in solving for forces in pulley systems.

Pulley Systems

Pulley systems are used to change the direction of an applied force, and in ideal situations such as massless, frictionless pulleys, the tension remains the same on both sides of the pulley. Understanding the behavior of pulley systems is essential for determining forces and mechanical advantages in static and dynamic problems.

Net Force on a Pulley

When a cable wraps around a pulley, the segments of the cable exert forces on the pulley. For instances where the cable wraps halfway around, the net force acting on the pulley is twice the tension in the cable. This concept is important in analyzing how forces are distributed in pulley arrangements and ensuring that the system remains in equilibrium.

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