Question

A block of mass 2 kg is connected to a freely hanging block of mass 4 kg by a light and inextensible string which passes over pulley at the edge of a table. the 2kg mass is on the surface of the table assumed to be smooth. calculate the acceleration of the system and the tension in the string
options
a) 6.7 m/s2 and 13.3 N
b) 3.3 m/s2 and 34.4 N
c) 0.54 m/s2 and 40.6 N
d) 2.5 m/s 2 and 32.2 N

Answer 1

Answer on Question #47906-Physics-Mechanics-Kinematics-Dynamics

A block of mass $2\mathrm{kg}$ is connected to a freely hanging block of mass $4\mathrm{kg}$ by a light and inextensible string which passes over pulley at the edge of a table. The $2\mathrm{kg}$ mass is on the surface of the table assumed to be smooth. Calculate the acceleration of the system and the tension in the string options

a) $6.7\mathrm{m / s2}$ and 13.3 N

b) $3.3\mathrm{m / s2}$ and 34.4 N

c) $0.54\mathrm{m / s2}$ and 40.6 N

d) $2.5\mathrm{m / s2}$ and 32.2 N

Solution

The blocks are connected by a string.

The tension due to the string is the same at both ends ("one string - one tension") so as the $4\mathrm{kg}$ block accelerates downwards the $2\mathrm{kg}$ block will accelerate across at the same rate.

We label this tension $T$ (because we're an imaginative bunch we are).

For the $3\mathrm{kg}$ mass: $= 2a$

For the $4\mathrm{kg}$ mass: $4g - T = 4a$

Now sub $T = 2a$ into the second equation to get $40 - 2a = 4a$ [taking $g = 10ms^{-2}$ at ordinary level]

Solve to get $a = 6.7\frac{m}{s^2}$

Now sub this value for $a$ into the $T = 2a$ equation to get $T = 13.3N$ .

Answer: a) $6.7 \frac{m}{s^2}$ and $13.3 \, \text{N}$ .

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