What is the net force (in N) on a ball with a mass of 19.5kg and volume of 1.0m3 when it is submerged under water? ρH2O=1000kg/m3 and g = 9.8m/s2. Answer to 1 decimal place and only put in the numerical value. Do not write the unit in your answer.

This is a short-answer question. Show all working on paper, including the relevant equations and units.

Question

What is the net force (in N) on a ball with a mass of 19.5kg and volume of 1.0m3 when it is submerged under water? ρH2O=1000kg/m3 and g = 9.8m/s2. Answer to 1 decimal place and only put in the numerical value. Do not write the unit in your answer.

This is a short-answer question. Show all working on paper, including the relevant equations and units.

BlackTom AI · Accepted Answer

The problem asks for the net force on a submerged ball. To analyze this, I’ll use the concept that the net force is the difference between the weight of the ball (downward) and the buoyant force (upward) due to displaced water.

First, identify the given quantities: mass m = 19.5 kg, volume V = 1.0 m^3, density of water ρ = 1000 kg/m^3, gravitational acceleration g = 9.8 m/s^2.

1) Weight of the ball (W): W = m g = 19.5 kg × 9.8 m/s^2 = 191.1 N. This force acts downward.

2) Buoyant force (F_b): This is equal to the weight of the displaced water, F_b = ρ g V = (1000 kg/m^3) × (9.8 m/s^2) × (1.0 m^3) = 9800 N. This force acts upward.

3) Net force (F_net): F_net = W − F_b if we take downward as positive, or F_net = F_b − W if we take upward as positive. The magnitude is |F_b − W|. Substituting the values: |9800 N − 191.1 N| = 9608.9 N.

4) Direction: Since the buoyant force greatly exceeds the weight, the net force acts upward, opposing the weight of the ball.

5) Numerical result (to appropriate precision): The magnitude of the net force is 9608.9 N, and its direction is upward. If a single numeric value without units is requested, this corresponds to the magnitude 9608.9 (and it would be stated as upward in context).

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