Solve problems involving force due to gravity (weight) and mass using 𝐹𝑔 = 𝑚𝑔.

A sports equipment manufacturer tests a new basketball design by measuring the contact force between the ball and a digital force platform during a bounce. The ball has a mass of 624 g. When the ball is at rest on the platform, the platform records a normal force of 6.12 N. During a bounce test, the platform records a peak normal force of 43.7 N at the moment of maximum compression. Determine the apparent weight of the ball at the moment of maximum compression, and calculate the net upward force acting on the ball at that instant. Show your working.

A shipping container with a mass of 2,450 kg is lifted by a crane at a construction site. Calculate the force due to gravity acting on the container. Show your working.

A package with a mass of 8.5 kg is placed on the Moon's surface. Calculate the gravitational force acting on the package. Show your working. (Use g = 1.6 m s⁻² for the Moon.)

A cylindrical fuel tank has a mass of 450 kg when empty. When filled with liquid hydrogen, the combined mass of the tank and fuel is 1,350 kg. The tank is lifted vertically by a crane on Earth's surface. Calculate the magnitude of the additional gravitational force exerted on the crane due to the fuel alone. (Take \(g = 9.8\,\text{m/s}^2\).)