Question

Two masses mA = 1.0 kg and mB = 7.0 kg are on inclines and are connected together by a string as shown in (Figure 1). The coefficient of kinetic friction between each mass and its incline is μk = 0.30.
If mA moves up, and mB moves down, determine their acceleration. Ignore masses of the (frictionless) pulley and the cord.

Answer 1

Answer on Question #85208, Physics / Mechanics | Relativity

Question:

Two masses $\mathrm{mA} = 1.0\mathrm{kg}$ and $\mathrm{mB} = 7.0\mathrm{kg}$ are on inclines and are connected together by a string as shown in (Figure 1). The coefficient of kinetic friction between each mass and its incline is $\mu \mathrm{k} = 0.30$ .

If mA moves up, and mB moves down, determine their acceleration. Ignore masses of the (frictionless) pulley and the cord.

Solution:

Equations of mass motion are: $m_{B}a = m_{B}g\sin \beta -\mu_{k}m_{B}g\cos \beta -T$ and $m_Aa = T - m_Ag\sin \alpha -\mu_km_Ag\cos \alpha$ , respectively the acceleration $a = g\frac{(m_B\sin\beta - m_A\sin\alpha) - \mu_k(m_A\cos\alpha + m_B\cos\beta)}{m_A + m_B}$ . Using known parameters we get: $a = 10\frac{(7\sin\beta - \sin\alpha) - 0.3(\cos\alpha + 7\cos\beta)}{8}$

The answer:

The acceleration is: $a = 10\frac{(7\sin\beta - \sin\alpha) - 0.3(\cos\alpha + 7\cos\beta)}{8}$ .

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