Answer to Question #102353 in Electricity and Magnetism for Ali hamza

Question #102353
A ball of mass m1 and a block of mass m2 are attached by a lightweight cord that passes
over a frictionless pulley of negligible mass, as in figure below. The block lies on a frictionless incline of
angle θ. Find the magnitude of the acceleration of the two objects and the tension in the cord.
1
Expert's answer
2020-10-15T02:32:10-0400


Write all forces by their axes along which the acceleration is directed according to Newton's second law:


Block: m2a=m2g sinθT,Ball: m1a=Tm1g.\text{Block: }m_2a=m_2g\text{ sin}\theta-T,\\ \text{Ball: }m_1a=T-m_1g.

Divide one by another:


m2m1=m2g sinθTTm1g, T=gm1m2(1+sinθ)m1+m2.\frac{m_2}{m_1}=\frac{m_2g\text{ sin}\theta-T}{T-m_1g},\\ \space\\ T=g\cdot\frac{m_1m_2(1+\text{sin}\theta)}{m_1+m_2}.

Acceleration, on the other hand, will be


a=Tm1g, a=g[m2(1+sinθ)m1+m21], a=gm2 sinθm1m1+m2.a=\frac{T}{m_1}-g,\\ \space\\ a=g\bigg[\frac{m_2(1+\text{sin}\theta)}{m_1+m_2}-1\bigg],\\ \space\\ a=g\cdot\frac{m_2\text{ sin}\theta-m_1}{m_1+m_2}.

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Comments

RANGOJIRE OKOK
26.06.22, 19:19

This answer very interesting to me. Thank you so much

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