Final answer:
The gravitational force acting on a 8 cm long piece of tape is calculated using the formula F = mg, where g is the acceleration due to gravity. The tape's mass is first determined to be 6.4 × 10^-6 kg, and then the force is found to be 6.272 × 10^-5 Newtons.
Step-by-step explanation:
The magnitude of the gravitational force acting on the tape can be calculated using Newton's law of gravitation, which is given by the formula F = GmM, where F is the force, G is the gravitational constant, m and M are the masses of the objects. Since we only need the force due to the Earth's gravity on the tape, we can simplify this as the weight of the tape, with F = mg, where g is the acceleration due to gravity, which is approximately 9.8 m/s².
First, we need to determine the mass of the tape. The mass of 1 meter of tape is given as 0.08 g, so the mass of 8 cm (or 0.08 m) of tape would be:
m = (0.08 g/m) × 0.08 m = 0.0064 g
To use SI units, we convert this into kilograms:
m = 0.0064 g × (1 kg / 1000000 g) = 6.4 × 10^-6 kg
Now, we can calculate the gravitational force:
F = mg = (6.4 × 10^-6 kg) × 9.8 m/s² = 6.272 × 10^-5 N.