Concept explainers
A package is thrown down an incline at A with a velocity of 1 m/s. The package slides along the surface ABC to a conveyor belt that moves with a velocity of 2 m/s. Knowing that d = 6 m and μk = 0.2 between the package and all surfaces, determine (a) the speed of the package at C, (b) the distance the package will slide on the conveyor belt before it comes to rest relative to the belt.
(a)
Find the speed
Answer to Problem 13.12P
The speed
Explanation of Solution
Given information:
The velocity of conveyor
The coefficient of the static friction between package with surface
The distance between the point C to point B
The inclined angle of the member BA
The velocity at the point A
The distance between the point A to B (d) is
Assume the acceleration due to gravity (g) is
Calculation:
Calculate the weight of the conveyor (W) using the formula:
Substitute
Show the free body diagram of the package sliding from the corner A to B as in Figure (1).
Calculate the normal force at point AB
Substitute
Calculate the force at point AB
Substitute
Calculate the work done
Substitute
Show the free body diagram of the package sliding from corner B to C as in Figure (2).
Calculate the normal force at point BC
Substitute
Calculate the force at point BC
Substitute
Calculate the work done
Substitute
Assume the corner B has no energy.
Use work and energy principle which states that kinetic energy of the particle at a displaced point can be obtained by adding the initial kinetic energy and the work done on the particle during its displacement.
Find the speed
Substitute
Substitute
Therefore, the speed
(b)
Find the distance
Answer to Problem 13.12P
The distance
Explanation of Solution
Given information:
The velocity of conveyor
The coefficient of the static friction between package with surface
The distance between the point C to point B
The inclined angle of the member BA
The velocity at the point A
The distance between the point A to B (d) is
Assume the acceleration due to gravity (g) is
Calculation:
Calculate the force (F) using the formula:
Substitute
Calculate the work done
Here,
Substitute
Use work and energy principle which states that kinetic energy of the particle at a displaced point can be obtained by adding the initial kinetic energy and the work done on the particle during its displacement.
Find the distance
Substitute
Substitute
Therefore, the distance
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Chapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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