Dynamic problem Vector Mechanics for Engineers: Dynamics 10th ed 12. 30 the coef
ID: 1824164 • Letter: D
Question
Dynamic problem Vector Mechanics for Engineers: Dynamics 10th ed 12. 30 the coefficient of friction between blocks a and c and the horizontal surfaces are /mu s = 0.24 and /mu k = 0.20. Knowing that Ma = 5 kg Mb = 10 kg and mc = 10kg (a) the tension in the cord (b) the acceleration of each block
Dynamic problem Vector Mechanics for Engineers: Dynamics 10th ed 12. 30 the coefficient of friction between blocks a and c and the horizontal surfaces are /mu s = 0.24 and /mu k = 0.20. Knowing that Ma = 5 kg Mb = 10 kg and mc = 10kg (a) the tension in the cord (b) the acceleration of each blockExplanation / Answer
The constraint relation between blocks A,B and C gives,
Ab = Aa/2 + Ac/2 (where A is acceleration of block)
Case 1
All blocks are in rest
T - fa = 0
T - fc = 0
2T = Mb * g
so
T = 10 * 10/2 = 50 N
so
fa = fc = 50 N
But
Max fa = 5 * 10 * 0.24 = 12 N
so since required fa > max fa
all blocks cannot be in rest position
Case 2
Block C is in rest
T - fa = ma * Aa
T - fc = 0
mb * g - 2T = mb * Ab
fa = ma * g * uk = 5 * 10 * 0.2 = 10 N
T - 10 = 5 * Aa
10 * 10 - 2T = 10 * Ab
but Ab = Aa/2 + 0/2 = Aa/2
T - 10 = 5 * Aa ---(1)
100 - 2T = 5 * Aa ---(2)
2 * (1) + (2)
100 - 20 = 10 * Aa + 5 * Aa
15 * Aa = 80
Aa = 16/3 m/s
so
T = 5 * 16/3 + 10 = 110/3
so
fc = 110/3 = 36.67 N
but
Max fc = 10 * 10 * 0.24 = 24 N
So Block C cannot be in rest
CASE 3
ALL blocks are in motion
For Block A
T - fa = ma * Aa
T - 5 * 10 * 0.2 = 5 * Aa
T - 10 = 5 * Aa ---(1)
For Block C
T - fc = mc * ac
T - 10 * 10 * 0.2 = 10 * Ac
T - 20 = 10 * Ac ----(2)
For Block B
mb g - 2T = mb * Ab
10 * 10 - 2T = 10 * Ab
100 - 2T = 10 * Ab
but Ab = Aa/2 + Ac/2
100 - 2T = 5 * Aa + 5 * Ac ----(3)
3 * (2) + (3) - (1) gives
100 + 10 - 3 * 20 = 3 * 10 * Ac + 5 * Ac
35 * Ac = 50
Ac = 10/7 m/s
so
T = 20 + 10 * 10/7 = 240/7 N
Aa = (240/7 - 10)/5 = 34/7 m/s
Ac = (10/7 + 34/7)/2 = 22/7 m/s
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