Concept explainers
a)
Find the angular velocity of the bar after the impact.
a)
Answer to Problem 17.130P
The angular velocity of the bar after the impact is
Explanation of Solution
Given information:
The weight
The radius
The weight
The length
The angular velocity
The velocity
Calculation:
Consider G is the mass center of rod AB.
Find the mass
Substitute 2 lb for
Find the moment of inertia
Substitute
Consider C be the mass center of the sphere.
Find the mass of the sphere
Substitute 3 lb for
Find the moment of inertia
Substitute
The rod and sphere have same angular velocity
Sketch the geometry of the sphere and the uniform rod as shown in Figure (1).
Refer Figure (1),
Find the distance R.
Substitute 10 in. for L and 3 in. for r.
Find the angle
Substitute 10 in. for L and 3 in. for r.
Find the velocity
Substitute 10 in. for L and
Write the velocity
Write the velocity
Consider the conservation of momentum principle.
Sketch the impulse and momentum diagram of the system as shown in Figure (2).
Refer Figure (2).
Take moment about A (positive sign in clockwise direction).
Substitute
Substitute
Thus, the angular velocity of the bar after the impact is
b)
Find the components of the reactions at A.
b)
Answer to Problem 17.130P
The horizontal component of the reactions at A is
The vertical component of the reactions at A is
Explanation of Solution
Calculation:
Find the normal acceleration
Substitute 10 in. for L and
Write the equation of tangential acceleration
Here,
Substitute 10 in. for L.
Find the normal acceleration
Substitute 0.8700 ft for R and
Write the equation of tangential acceleration
Substitute 0.8700 ft for R.
Sketch the free body diagram of the uniform rod and sphere as shown in Figure (1).
Refer Figure (3).
Take moment about A (positive sign in clockwise direction).
Substitute
Substitute 2 lb for
Find the tangential acceleration
Substitute
Find the tangential acceleration
Substitute
Refer Figure (3),
Consider the horizontal component forces.
Here,
Substitute
Thus, the horizontal component of the reactions at A is
Consider vertical components of forces.
Here,
Substitute 2 lb for
Thus, the vertical component of the reactions at A is
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Chapter 17 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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