Question

The catapulting mechanism is used to propel the 10 -kg slider $A$ to the right along the smooth track. The propelling action is obtained by drawing the pulley attached to rod $B C$ rapidly to the left by means of a piston $P .$ If the piston applies a constant force $F=20 \mathrm{kN}$ to rod $B C$ such that it moves it $0.2 \mathrm{m}$, determine the speed attained by the slider if it was originally at rest. Neglect the mass of the pulleys, cable, piston, and rod $B C$

Name: Problem 26, Chapter 14: Engineering Mechanics: Dynamics
Uploaded: 2024-04-02T10:26:39-08:00
Duration: 2 min 29 s
Channel: Narayan Hari

   The catapulting mechanism is used to propel the 10 -kg slider $A$ to the right along the smooth track. The propelling action is obtained by drawing the pulley attached to rod $B C$ rapidly to the left by means of a piston $P .$ If the piston applies a constant force $F=20 \mathrm{kN}$ to rod $B C$ such that it moves it $0.2 \mathrm{m}$, determine the speed attained by the slider if it was originally at rest. Neglect the mass of the pulleys, cable, piston, and rod $B C$

Engineering Mechanics: Dynamics

R. C. Hibbeler 14th Edition

Chapter 14, Problem 26

Instant Answer

Solved by Expert Narayan Hari

04/02/2024

Step 1

- Mass of the slider $ A $, $ m = 10 \, \text{kg} $. - Constant force applied by the piston, $ F = 20 \, \text{kN} = 20000 \, \text{N} $. - Distance moved by the rod $ BC $, $ d = 0.2 \, \text{m} $. - Initial velocity of the slider, \( v_0 = 0 \, Show more…

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The catapulting mechanism is used to propel the 10 -kg slider $A$ to the right along the smooth track. The propelling action is obtained by drawing the pulley attached to rod $B C$ rapidly to the left by means of a piston $P .$ If the piston applies a constant force $F=20 \mathrm{kN}$ to rod $B C$ such that it moves it $0.2 \mathrm{m}$, determine the speed attained by the slider if it was originally at rest. Neglect the mass of the pulleys, cable, piston, and rod $B C$

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Key Concepts

Work?Energy Principle

The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy. This principle allows us to determine the final velocity of an object by equating the work done on it to the increase in its kinetic energy, especially when the object starts from rest.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion, expressed by the formula (1/2)mv². In this type of problem, calculating the kinetic energy helps in understanding how the work provided by the applied force has been converted into the motion of the object.

Work

Work is defined as the product of a force and the displacement in the direction of that force. In problems like this, where a constant force is applied over a specific distance, the work done is calculated by multiplying the force and the displacement. This concept is crucial in understanding how mechanical energy is added to a system.

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