Final answer:
To calculate the height, use the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. For the given values of mass and change in potential energy, the object needs to be lifted approximately 2.1 meters.
Step-by-step explanation:
To calculate the height, we need to find the change in gravitational potential energy. The formula for gravitational potential energy is given by PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height.
We're given that the gravitational potential energy increases by 41.16 J, and the mass of the object is 2.0 kg. Plugging these values into the formula, we get 41.16 J = (2.0 kg)(9.8 m/s²)h. Solving for h, we find that h = 41.16 J / (2.0 kg)(9.8 m/s²) ≈ 2.1 m. Therefore, the object must be lifted approximately 2.1 meters on Earth for the gravitational potential energy to increase by 41.16 J.