Question

find the mass of block m if the system accelerates at 1m/s² to the right and the coefficient of friction is 0.15. 550g 500g m

Explanation:

Step1: Convert masses to kg

$m_1 = 550\ \text{g} = 0.55\ \text{kg}$, $m_2 = 500\ \text{g} = 0.50\ \text{kg}$, $a = 1\ \text{m/s}^2$, $\mu = 0.15$, $g = 9.8\ \text{m/s}^2$

Step2: Define net force equation

Net force: $(m_1 + M)g - m_2g - \mu Mg = (m_1 + m_2 + M)a$

Step3: Substitute known values

$(0.55 + M)9.8 - 0.50\times9.8 - 0.15\times9.8M = (0.55 + 0.50 + M)\times1$

Step4: Simplify left and right sides

Left: $5.39 + 9.8M - 4.9 - 1.47M = 0.49 + 8.33M$
Right: $1.05 + M$

Step5: Solve for M

$0.49 + 8.33M = 1.05 + M$
$8.33M - M = 1.05 - 0.49$
$7.33M = 0.56$
$M = \frac{0.56}{7.33} \approx 0.0764\ \text{kg}$

Answer:

The mass of block M is approximately $0.076\ \text{kg}$ (or 76 g)