An empty plastic box of mass 9 kg is found to accelerate up at the rate of g/3 m/sec2 when placed deep inside water. Mass of the sand that should be put inside the box so that it may accelerate down at the rate of g/4 m/sec2 is
Lets do this the long way.
In the water, the net force=mass*acceleration (neglecting considerable friction).
but net force=bouyantforce-mg or
bouyant force=mass*g* 1/3 +mg=4/3 mg
this bouyant force does not change. So to go now,
bouyant force-(m+Masssand)g=-1/4 (M+m)
4/3 mg-mg-Mg=-1/4 mg
Mg=mg(.25+1.33)
solve for M
check all this.
To solve this problem, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
First, let's determine the net force acting on the plastic box when it accelerates up at the rate of g/3 m/sec^2. The net force is given by the equation:
Net force = mass * acceleration
Where mass is the mass of the plastic box, and acceleration is the given value (g/3 m/sec^2). Rearranging the equation, we have:
Net force = 9 kg * (g/3 m/sec^2) = 3g Newtons
Now, let's find the mass of the sand that should be added to the box to make it accelerate down at the rate of g/4 m/sec^2. In this case, the net force acting on the box will be in the opposite direction. Therefore, the net force equation becomes:
Net force = mass * acceleration
Given the acceleration (g/4 m/sec^2), we want the net force to be in the opposite direction as before. Hence, the net force is equal to -3g Newtons.
Using the same equation, we can rearrange it to solve for the mass:
mass = Net force / acceleration
mass = (-3g) / (g/4)
mass = -12 kg
Since mass cannot be negative, we conclude that no amount of sand can be added to the box to achieve the desired acceleration.