A balloon is tied to a block. The mass of the block is $$2$$ kg. The tension of the string between the balloon and the block is $$30$$ N. Due to the wind, the string has an angle θ relative to the vertical direction, $$cos$$θ $$=$$ $$4/5$$ and $$sin$$θ $$=$$ $$3/5$$. Assume the acceleration of gravity is g $$=$$ $$10$$ $$m/s2$$. Also assume the block is small so the force on the block from the wind can be ignored. Then the $$y-component$$ and the $$y-component$$ of the acceleration a of the block.

Question

A balloon is tied to a block. The mass of the block is $$2$$ kg. The tension of the string between the balloon and the block is $$30$$ N. Due to the wind, the string has an angle θ relative to the vertical direction, $$cos$$θ $$=$$ $$4/5$$ and $$sin$$θ $$=$$ $$3/5$$. Assume the acceleration of gravity is g $$=$$ $$10$$ $$m/s2$$. Also assume the block is small so the force on the block from the wind can be ignored. Then the $$y-component$$ and the $$y-component$$ of the acceleration a of the block.

Infinity Learn · Accepted Answer

The magnitude of the force (from$$ the $$string) is $$T=30$$ NThe $$x-component$$ $$=Tsin$$⁡θ$$=30$$×$$3/5=18NThey-component$$ $$=Tcos$$⁡θ$$=30$$×$$4/5=24NThe$$ total force on the block is:The $$x-component$$ $$=$$ $$18$$ NThe $$y-component$$ $$=24$$−$$mg=24$$−$$20=4NThe$$ $$x-component$$ of the acceleration $$=18N/2kg=9m/s2The$$ $$y-component$$ of the acceleration $$=4N/2kg=2m/s2$$

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