Question 8. The mass of the object is approximately 36.091 grams.
Explanation for question 8. The formula for gravitational potential energy is given by:
GPE = mgh
where GPE is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height to which the object was lifted.
We can rearrange the formula to solve for m:
m = GPE / (gh)
Plugging in the values given, we have:
m = 4321 J / (9.8 m/s^2 * 1234 cm)
Converting the height to meters and expressing the mass in grams, we get:
m = 4321 J / (9.8 m/s^2 * 12.34 m) = 4321 J / 119.852 m^2/s^2 = 36.091 grams
Therefore, the mass of the object is approximately 36.091 grams.
Question 9. The value of gravity on the unknown planet is approximately 15.16 m/s^2.
Explanation for question 9. The gravitational potential energy of an object is given by the equation:
GPE = mass * gravity * height
Rearranging this equation to solve for gravity, we get:
gravity = GPE / (mass * height)
Plugging in the values you provided, we get:
gravity = 190 J / (150 g * 1.9 m)
Converting the mass to kilograms (150 g = 0.15 kg) and performing the calculation, we find that the value of gravity on the unknown planet is approximately 15.16 m/s^2.
Question 10. The value of gravity on the unknown planet is approximately 10.3 m/s^2.
Explanation for question 10. In order to find the value of gravity on the unknown planet, you need to use the formula for gravitational potential energy (GPE), which is:
GPE = mass * gravity * height
You can rearrange this formula to solve for gravity:
gravity = GPE / (mass * height)
Plugging in the values you provided, you get:
gravity = 250 J / (183 g * 2.8 m)
Solving this equation, you find that the value of gravity on the unknown planet is approximately 10.3 m/s^2.