First slide

Newton's laws of motion

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.

Difficult

A

$9 m / s^{2}, 2 m / s^{2}$
B

$9 m / s^{2}, 12 m / s^{2}$
C

$18 m / s^{2}, 2 m / s^{2}$
D

$18 m / s^{2}, 12 m / s^{2}$

Solution

The magnitude of the force (from the string) is T=30 N
The x-component $= T \sin θ = 30 \times 3 / 5 = 18 N$
They-component $= T \cos θ = 30 \times 4 / 5 = 24 N$
The total force on the block is:
The x-component = 18 N
The y-component $= 24 - m g = 24 - 20 = 4 N$
The x-component of the acceleration $= 18 N / 2 kg = 9 m / s^{2}$
The y-component of the acceleration $= 4 N / 2 kg = 2 m / s^{2}$

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