I'm super confused about how to approach this problem. Please help.
A ball of Styrofoam (ρ = 100 kg/m3) is totally submerged in water. The ball has a mass of 300.0 g
What is the volume of the ball?
If a string holds the ball when it’s in the water, what’s the tension in the string?
Okay, I figured out the volume, I just need help finding the tension. What should I do to find that?
Vs = 0.3kg * 1m^3/100kg = 0.003 m^3 =
Vol. of Styrofoam = Vol. of water Dis-
placed.
Mass = 0.003m^3 * 100kg/m^3 = 0.3 kg.
T = 0.3kg * 9.8N/kg = 2.94 N.
Note: Density of water = 1000kg/m^3.
To solve the first part of the problem and find the volume of the ball, we can use the formula:
Density (ρ) = Mass (m) / Volume (V)
Rearranging the formula, we have:
Volume (V) = Mass (m) / Density (ρ)
Given that the mass of the Styrofoam ball is 300.0 g and the density of Styrofoam is 100 kg/m3, we need to convert the mass to kilograms before substituting the values into the formula:
300.0 g = 300.0 g * (1 kg / 1000 g) = 0.3 kg
Now, substituting the values into the formula, we get:
Volume (V) = 0.3 kg / 100 kg/m3 = 0.003 m3
Therefore, the volume of the Styrofoam ball is 0.003 cubic meters.
Moving on to the second part of the problem, we need to calculate the tension in the string when the ball is submerged in water. In this scenario, the string must exert an upward force equal to the weight of the ball, which is given by the formula:
Weight (W) = Mass (m) * Acceleration due to gravity (g)
Given that the mass of the ball is 300.0 g, we convert it to kilograms:
300.0 g = 0.3 kg
The acceleration due to gravity, denoted by 'g', is approximately equal to 9.8 m/s2.
Now, using the formula for weight, we can find:
Weight (W) = 0.3 kg * 9.8 m/s^2 = 2.94 N
Therefore, the tension in the string while holding the ball in water is 2.94 Newtons.