Question

Block B starts from rest, block A moves with a constant acceleration, and slider block C moves to the right with a constant acceleration of 75 mm/s2. Knowing that at t = 2 s the velocities of B and C are 480 mm/s downward and 280 mm/s to the right, respectively, determine (a) the accelerations of A and B, (b) the initial velocities of A and C, (c) the change in position of slider block C after 3 s.

Answer 1

Answer:  Block B starts from rest, block A moves with a constant acceleration, and slider block C moves to the right with a constant acceleration of 75 mm/s^2. Knowing that at t = 2 s the velocities of B and C are 480 mm/s downward and 280 mm/s to the right, respectively, determine (a) the accelerations of A and B. (b) the initial velocities of A and C, (c) the change in position of slider block C after 3 s. Block B moves downward with a constant velocity of 20 mm/s. At t = 0, block A is moving upward with a constant acceleration, and its velocity is 30 mm/s. Knowing that at t = 3 s slider block C has moved 57 mm to the right, determine (a) the velocity of slider block

Explanation:

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Answer 2

Answer:

a ) acceleration of A -345mm/s^2, acceleration of B 240 mm/s^2 (b) velocity of A -43.3mm/s ,velocity of C is 130 mm/s (c) change in position of slider block C is 728 mm

Explanation:

3Ya +4Yb+Xc = constant

then 3Va+4Vb+Vc = constant

then 3Aa+4Ab+Ac = constant

(a) Aa and Ac are constant therefore Ab will also be constant

Vb = 0+ Abt

At t = 2sec 480 mm/s = 0+ Ab2

Ab = 240 mm/s^2

3Aa+4Ab + Ac = 0

3Aa+ 4 ×240 + 75 = 0

Aa = -345mm/s^2

(b) we have Vc = Vc(0) + Abt

at t =2 sec 280 = Vc(0)+ 75 ×2

Vc(0) = 130 mm/s

now 3Va(0)+ Vb + Vc =0

3Va(0) + 0 + 130 = 0

Va = -43.3mm/s

(c) Xc = Vc(0)t + 1/2Act^2

Xc = 130 ×3 +1/2 ×75 ×3×3

Xc = 728 mm