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Question bank: Dynamics: Traction Force

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Question 1:

Hard

A body of mass 20 kg is supported on a perfectly smooth horizontal surface, connected by an inelastic cable to another body of mass 10 kg hanging vertically down next to an ideal pulley, as shown in the figure. Considering that the acceleration due to gravity is 10 m/s² and neglecting the mass of the cable and the existence of friction, determine the tension force in the cable and the acceleration of the bodies. Explain, based on the concept of conservation of mechanical energy, what would happen to the velocity of the bodies if the cable broke during the motion, indicating why mechanical energy would no longer be conserved in that case.
Dynamics: Traction Force
Question 2:

Medium

A block of mass 5 kg is supported on a perfectly smooth horizontal surface. A horizontal force F is applied to it, pulling it through an inextensible and negligible mass wire. The block accelerates with a constant acceleration of 3 m/s². Determine the tension force in the wire and its angle with respect to the horizontal. Consider g = 10 m/s² and sin(θ) = 0.6, where θ is the angle formed by the wire with the horizontal.
Dynamics: Traction Force
Question 3:

Medium

The city of Salvador, famous for its hills and elevators, is a perfect example to demonstrate the force of traction. The Lacerda Elevator, one of the main postcards of the city, transports thousands of people daily between the Upper Town and the Lower Town. Suppose one day, a group of 15 people with an average mass of 70kg decide to use the elevator at the same time. Considering the elevator's mass as 500kg and the acceleration due to gravity equal to 10 m/s², what would be the traction force on the elevator cable when it is at rest or moving at a constant speed?
Dynamics: Traction Force
Question 4:

Medium

Dynamics: Traction Force
Question 5:

Very Hard

A block of mass 2 kg is attached to a cable and is pulled by a constant horizontal force. The angle between the cable and the horizontal direction of the block is 30 degrees. The coefficient of kinetic friction between the block and the surface is 0.2. Determine the tension force in the cable that accelerates the block at a rate of 2 m/s^2. Consider the acceleration due to gravity as 10 m/s^2 and neglect the mass of the cable and air resistance.
Dynamics: Traction Force
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