Question

unit 2 exam mcq portion (10 question version)
(a) 2n
(b) 6n
(c) 8n
(d) 16n
(e) 24n
two 4 kg blocks hang from a rope that passes over two frictionless pulleys, as shown in the figure above. what is the tension in the horizontal portion of the rope if the blocks are not moving and the rope and the two pulleys have negligible mass?
(a) 4n
(b) 8n
(c) 20n
(d) 40n
(e) 80n
three blocks of masses m, 3m, and 2m resting on a frictionless horizontal surface are connected to identical ideal springs, as shown above. a force of magnitude f directed to the left is then applied to the left - end of spring a. which spring is stretched the most when the blocks are all moving with the same acceleration?
(a) a
(b) b
(c) c
none, because the springs do not stretch.
none, because the springs all stretch the same amount.

Explanation:

Step1: Analyze the first - pulley problem

For the two - block pulley system, since the blocks are not moving and the ropes and pulleys are massless, consider the equilibrium of one of the blocks. The force of gravity on a 4 kg block is $F = mg$, where $g = 10m/s^{2}$ (approximate value on Earth's surface). So $F=4\times10 = 40N$. In equilibrium, the tension in the rope is equal to the force of gravity acting on one of the hanging blocks.

Step2: Analyze the second - spring problem

First, find the acceleration of the whole system. The total mass of the system is $m + 3m+2m=6m$. According to Newton's second law $F = ma$, the acceleration of the system $a=\frac{F}{6m}$. Then, consider the forces on each block - spring combination. For spring A, the force causing its stretch is $F$. For spring B, the force causing its stretch is the force needed to accelerate the mass $3m + 2m=5m$ to the left, so $F_B=(3m + 2m)a=(5m)\times\frac{F}{6m}=\frac{5F}{6}$. For spring C, the force causing its stretch is the force needed to accelerate the mass $2m$ to the left, so $F_C = 2ma=2m\times\frac{F}{6m}=\frac{F}{3}$. Since $F>F_B>F_C$, spring A is stretched the most.

Answer:

For the first question: D. 40 N
For the second question: A. A