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A balloon with its contents weighing 160 N is moving down with an acceleration of g/2 m/s². The mass to be removed from it so that the balloon moves up with an acceleration of m/s² is 2x where x is?
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A balloon with its contents weighing 160 N is moving down with an acce...
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A balloon with its contents weighing 160 N is moving down with an acceleration of g/2 m/s².
Calculating the Mass of the Balloon
To find the mass of the balloon, we can use the formula:
Weight = Mass * Acceleration due to gravity
Given that the weight of the balloon is 160 N and the acceleration due to gravity is g/2 m/s², we can write the equation as:
160 = Mass * (g/2)
Simplifying the equation, we get:
Mass = 320/g
Calculating the Mass to be Removed
To calculate the mass to be removed from the balloon so that it moves up with an acceleration of m/s², we need to consider the forces acting on the balloon.
When the balloon moves down with an acceleration of g/2 m/s², the net force acting on it is given by:
Net Force = Mass * Acceleration
Net Force = Mass * (g/2)
Since the balloon is moving down, the net force is equal to the weight of the balloon minus the force exerted by the contents of the balloon:
Net Force = Weight - Force exerted by contents
Mass * (g/2) = 160 - Force exerted by contents
The force exerted by the contents is given by:
Force exerted by contents = mass of contents * acceleration
Substituting the mass of the contents as 2x and the acceleration as m/s², we get:
Mass * (g/2) = 160 - 2x * m
Simplifying the equation, we have:
320/g = 160 - 2xm
Solving for x, we get:
2x = (320/g - 160)/m
Therefore, x = (160/g - 80)/m
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A balloon with its contents weighing 160 N is moving down with an acceleration of g/2 m/s². The mass to be removed from it so that the balloon moves up with an acceleration of m/s² is 2x where x is?
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