Question

1. two blocks, with masses m₁ and m₂ = 12 kg, are connected by a string and move across a frictionless surface. a force f = 26.2 n is applied to block m₂. the tension in the string between them is t = 20 n

a. find the acceleration of each object.
b. find the mass of m₁.

Explanation:

Step1: Find acceleration via $m_2$

For block $m_2$, net force is $F - T$. Use $F_{net}=ma$.
$$a = \frac{F - T}{m_2} = \frac{26.2\ \text{N} - 20\ \text{N}}{12\ \text{kg}} = \frac{6.2}{12}\ \text{m/s}^2 \approx 0.52\ \text{m/s}^2$$

Step2: Find $m_1$ via tension

Tension $T$ accelerates $m_1$. Use $T = m_1a$.
$$m_1 = \frac{T}{a} = \frac{20\ \text{N}}{0.52\ \text{m/s}^2} \approx 38.46\ \text{kg}$$

Answer:

a. $0.52\ \text{m/s}^2$
b. $\approx 38.46\ \text{kg}$