Concept explainers
Race car A is traveling on a straight portion of the track while race car B is traveling on a circular portion of the track. At the instant shown, the speed of A is increasing at the rate of 10 m/s2, and the speed of B is decreasing at the rate of 6 m/s2. For the position shown, determine (a) the velocity of B relative to A, (b) the acceleration of B relative to A.
Fig. P11.141
(a)
The relative velocity
Answer to Problem 11.141P
The relative velocity
Explanation of Solution
Given Information:
The speed
The speed
The speed
The speed
The radius of the circular path
Calculation:
Convert unit kilometer per hour to meter per second.
Consider the velocity
Consider the velocity
Write the velocity of B
Write the velocity of A
Calculate the relative velocity vector
Substitute
Here,
Calculate the relative velocity
Substitute
Calculate the angle
Substitute
Therefore, the relative velocity
(b)
The relative acceleration
Answer to Problem 11.141P
The relative acceleration
Explanation of Solution
Given Information:
The speed
The speed
The speed
The speed
The radius of the circular path
Calculation:
Calculate the normal acceleration
Substitute
The normal acceleration at an angle:
Write the normal acceleration of B
Substitute
Write the tangential acceleration
Substitute
Write the tangential acceleration
The normal acceleration
Calculate the relative acceleration vector
Rewrite the above equation.
Substitute
Here,
Calculate the relative acceleration
Substitute,
Calculate the angle
Substitute,
Therefore, the relative acceleration
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Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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