Newton Duck Question?

Question

Three toy ducks, attached to each other by a string, are being pulled. The front duck has a mass of 1.0 kg, the second duck has a mass of 5.0 kg, the third duck has a mss of 2.0 kg. If the student pulls them with a force of 10 M and there is no friction, calculate the acceleration, the tension in the string connecting ducks 1 and 2, the tension in the string connecting ducks 2 and 3.

Answer 1

m1 = 1.0 kg
m2 = 5.0 kg
m3 = 2.0 kg
M = 8.0 kg


Since the force (10 N) is acting on all of the ducks, we know that

F = Ma or

a = F / M = 10 / 8 = 1.25 m/s²


If we look at each duck individually, we see the following.

Forces on first duck:
F_apply
-T1

Forces on second duck:
T1
-T2

Forces on third duck:
T2


We can work backwards to solve this.

We know that

T2 = m3 a
T2 = 2 * 1.25 = 2.5 N

T1 - T2 = m2 a
T1 = m2 a + T2
T1 = 5 * 1.25 + 2.5 = 8.75 N


To check, we can use the first duck.

F_apply - T1 = m1 * a
10 - 8.75 = 1 * 1.25
1.25 = 1.25

It checks and we're done.