On planet X, an object weighs 5.66 N. On
planet B where the magnitude of the free-fall
acceleration is 1.43 g (where g = 9.8 m/s
2
is
the gravitational acceleration on Earth), the
object weighs 18.46 N.
F = m a = m g
on X :
m gx = 5.66 so gx = 5.66/m
on B
m gb = 18.46 = m * 1.43 * 9.8
so
m = 18.46 / (1.43*9.8)
and
gx = 5.66/m = 5.66 *1.43* 9.8 / 18.46
To solve this problem, we can use the formula for weight:
Weight = mass x acceleration due to gravity
Let's assume the mass of the object is "m."
On planet X, the weight is given as 5.66 N.
5.66 N = m x acceleration due to gravity on planet X (Let's call it gX)
On planet B, the weight is given as 18.46 N.
18.46 N = m x acceleration due to gravity on planet B (1.43 g)
Now, let's solve for gX by rearranging the equation for planet X:
m x gX = 5.66 N
gX = 5.66 N / m
Similarly, let's solve for gB by rearranging the equation for planet B:
m x (1.43 g) = 18.46 N
gB = 18.46 N / (m x 1.43 g)
Now, we can equate gX and gB to find the relationship between the two:
5.66 N / m = 18.46 N / (m x 1.43 g)
Simplifying:
5.66 N = 18.46 N / 1.43
5.66 N = 12.9 N
Since this equation is not true, we can conclude that there was an error in the measurements or calculations.
To find the acceleration due to gravity on planet B, we can use Newton's second law of motion, which states that the weight of an object is equal to the mass of the object multiplied by the acceleration due to gravity.
Let's denote the weight of the object on planet X as W_x and the weight of the object on planet B as W_B. We are given the following information:
W_x = 5.66 N (weight on planet X)
W_B = 18.46 N (weight on planet B)
We can rearrange the equation for weight to solve for the acceleration due to gravity:
W = m * g
Where:
W is the weight of the object
m is the mass of the object
g is the acceleration due to gravity
Since the mass of the object is constant, we can write the equation as:
W_x / W_B = (m * g_x) / (m * g_B)
Dividing both sides by 'm' cancels out the mass:
W_x / W_B = g_x / g_B
Now, we can substitute the given values:
5.66 N / 18.46 N = g_x / g_B
Simplifying this equation, we can solve for g_B:
g_B = (18.46 N * g_x) / 5.66 N
g_B = (18.46 N * 9.8 m/s^2) / 5.66 N
g_B = 31.97 m/s^2
Therefore, the magnitude of the free-fall acceleration on planet B is 31.97 m/s^2.