Physics
A scientific instrument weighing 98 pounds on the Earth is transported to another planet whose mass is 1.7 Earth masses and whose radius is 0.7 Earth radii. What does this instrument weigh on this planet?
To be graded correctly, enter the new weight in pounds (numbers only, no text), rounded off to one decimal place. Your answer must be correct within ±0.5 pounds.
I got 339.99 or 340.0 lbs
98*1.7/.7^2=
and you are correct.
To calculate the weight of the instrument on the new planet, we can use the concept of gravitational force.
The formula for gravitational force is given by:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between two objects,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, the instrument is being transported to a planet with a different mass and radius compared to Earth.
Let's denote the weight of the instrument on Earth as W1 and the weight on the new planet as W2.
We can write the equation for the gravitational force on Earth as:
W1 = (G * m_instrument * m_earth) / r_earth^2
Similarly, the equation for the gravitational force on the new planet is:
W2 = (G * m_instrument * m_planet) / r_planet^2
Now, we can divide the equations to cancel out the gravitational constant, instrument mass, and rearrange for the ratio of the weights:
W2 / W1 = (m_planet / r_planet^2) / (m_earth / r_earth^2)
Given that the mass of the new planet (m_planet) is 1.7 times the mass of Earth, and the radius of the new planet (r_planet) is 0.7 times the radius of Earth, we can substitute these values into the equation:
W2 / W1 = (1.7 / 0.7^2) / 1
Simplifying further:
W2 / W1 = 1.7 / 0.49
W2 = W1 * (1.7 / 0.49)
Now, let's substitute the weight of the instrument on Earth, W1 = 98 pounds, into the equation:
W2 = 98 * (1.7 / 0.49)
Calculating further:
W2 = 339.99999999999994
Rounded to one decimal place, the weight of the instrument on the new planet would be approximately 340.0 pounds.
So, your answer of 340.0 pounds is correct. Well done!