buoyant force?

Question

If a ball of weight 9.54 N has a buoyant force of 0.69 N acting on it, what will the ball's actual acceleration (in m/s^2) be when the ball is dropped (ignoring air resistance)? Calculate your answer to the usual TWO DECIMAL PLACES. No, buoyant force isn't the same thing as air resistance! Your answer will be a negative number. HINT: A force diagram, and Newton's Second Law, will both be very helpful.

Answer 1

The ball's weight is the downward force acting on it due to gravity.
The buoyant force acting on the ball is due to the fact that the ball's value is displacing some of the surrounding fluid, which in turn exerts a force back, upward, on the ball equal to the weight of the displaced fluid.

The force of gravity (weight) is acting downward so we will call that the negative direction. The Buoyant force is acting upward, we will call that the positive direction.
To find the net force acting on the ball, add the two forces,
-9.54 N + .69 N = - 8.85 N

Thus the net force acting on the ball is 8.85 Newtons in the downward, negative, direction.

To find the acceleration experienced by the ball, use Newton's 2nd law,
F = ma
where F is the net force, m is the mass, and a is the acceleration,
a = F / m

To find the acceleration we need to find the ball's mass.
To find the ball's mass we can use the ball's weight (a force) and divide it by the gravitational acceleration,
W = mg
m = W / g
m = 9.54 N / 9.81 m/s^2
m = .97 kg

So now we know both the ball's mass and the net force acting on it,
a = F / m
a = -8.85 N / .97 kg
a = -9.41 m/s^2

The ball experiences an acceleration of 9.41 m/s^2 in the negative direction.

Answer 2

mrjeffy321 did a fine job of solving the problem and explaining each step.

I would just note that he made the assumption that the experiment occurs in a location where the acceleration of gravity is 9.8 m/s^2. Since that was not stated in the problem, perhaps it should not have been assumed. Or at least that assumption should be specifically stated in the solution.