A) On planet X, an object weighs 19.2 N. On planet B where the magnitude of the free-fall acceleration is 1.17 g (where g = 9.8 m/s2 is the gravitational acceleration on Earth), the object weighs 34.9 N.
The acceleration of gravity is 9.8 m/s2 . What is the mass of the object be on Earth? Answer in units of kg
B) What is the free-fall acceleration on planet X? Answer in units of m/s2
A. M*1.17g = 34.9 N.
M*1.17*9.8 = 34.9
M*11.47 = 34.9
M = 3.04 kg
B. 3.04 * a = 19.2 N.
a = 6.31 m/s^2 on planet X.
Note: It is the free-fall acceleration
that changes; the mass remains constant.
A) To find the mass of the object on Earth, we can use the formula:
Weight = mass x acceleration due to gravity
Given that the weight on Earth is 19.2 N and the acceleration due to gravity is 9.8 m/s^2, we can rearrange the formula to solve for mass:
Mass = Weight / acceleration due to gravity
Mass = 19.2 N / 9.8 m/s^2
Mass ≈ 1.96 kg
Therefore, the mass of the object on Earth is approximately 1.96 kg.
B) To find the free-fall acceleration on planet X, we can use the same formula as above:
Weight = mass x acceleration due to gravity
Given that the weight on planet X is 34.9 N and the mass of the object is still the same, we can rearrange the formula to solve for the acceleration:
Acceleration = Weight / mass
Acceleration = 34.9 N / 1.96 kg
Acceleration ≈ 17.8 m/s^2
Therefore, the free-fall acceleration on planet X is approximately 17.8 m/s^2.
A) To find the mass of the object on Earth, we can use the formula for weight:
Weight = mass * acceleration due to gravity
Given that the weight on Earth is 19.2 N and the acceleration due to gravity is 9.8 m/s^2, we can rearrange the formula to solve for mass:
mass = Weight / acceleration due to gravity
Plugging in the values, we have:
mass = 19.2 N / 9.8 m/s^2
mass ≈ 1.96 kg
Therefore, the mass of the object on Earth is approximately 1.96 kg.
B) To find the free-fall acceleration on planet X, we can compare the weight of the object on planet X to its weight on Earth. The weight of an object is proportional to the gravitational acceleration.
On planet B, the weight is 34.9 N and the acceleration due to gravity is 1.17 g. We can set up a proportion using these values:
Weight on planet B / acceleration on planet B = Weight on Earth / acceleration due to gravity
Simplifying the proportion gives:
Weight on planet B = (Weight on Earth * acceleration on planet B) / acceleration due to gravity
Plugging in the known values, we have:
34.9 N = (19.2 N * 1.17 g) / 9.8 m/s^2
To find the free-fall acceleration on planet X, we can rearrange the formula:
acceleration on planet X = (Weight on planet B * acceleration due to gravity) / Weight on Earth
Plugging in the known values, we have:
acceleration on planet X = (34.9 N * 9.8 m/s^2) / 19.2 N
Calculating this expression gives:
acceleration on planet X ≈ 17.88 m/s^2
Therefore, the free-fall acceleration on planet X is approximately 17.88 m/s^2.