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Q.

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, cosθ = 4/5 and sinθ = 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.

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a

9m/s2,2m/s2

b

9m/s2,12m/s2

c

18m/s2,2m/s2

d

18m/s2,12m/s2

answer is A.

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Detailed Solution

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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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, cosθ = 4/5 and sinθ = 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.