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A clarinetist, setting out for a performance, grabs his 3.39-kg clarinet case (including the clarinet) from the top of the piano and carries it through the air with an upward force of 34.9 N. Find the case\'s vertical acceleration. Indicate an upward acceleration as positive and a downward one as negative.
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from Fnet = ma
a = Fnet / m
and Fnet = Fa - Fw = 34.9 N - m g = 34.9 N - 3.39(9.81) = 1.644 N
so
a = 1.644 N / 3.39 kg = 0.485 m/s/s
round appropriately
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To determine the upward acceleration, we need to determine the net upward force on the clarinet. The net upward force is equal to the 34.9 N force minus the weight of the clarinet.
Weight = 3.39 * 9.8 = 33.222 N
Net upward force = 34.9 – 33.222 = 1.678 N
1.678 = 3.39 * a
a = 1.678 ÷ 3.39
The upward acceleration is approximately 0.5 m/s^2.
We have in the vertical the net lifting force, f = mA = L - W; so A = (L - W)/m = (34.9 - 3.39*9.8)/3.39 = 4.9499E-01 = .495 m/s^2. ANS.