A neutron star has a mass of 1.27 × 1030 kg (about the mass of our sun) and a radius of 6.47 × 103 m. Suppose an object falls from rest near the surface of such a star. How fast would it be moving after it had fallen a distance of 0.0086 m? (Assume that the gravitational force is constant over the distance of the fall, and that the star is not rotating.)
assume you mean Mstar = 1.27*10^30
and r = 6.47 * 10^3
(1/2) m v^2 = Fg * .0086
Fg = G Mstar * m / r^2
so
v^2 = (2 G Mstar/r^2).0086
A neutron star has a mass of 2.1 1030 kg (about the mass of our sun) and a radius of 6.2 103 m (about the height of a good-sized mountain). Suppose an object falls from rest near the surface of such a star. How fast would this object be moving after it had fallen a distance of 0.013 m? (Assume that the gravitational force is constant over the distance of the fall and that the star is not rotating.)
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To calculate the velocity of an object falling near the surface of a neutron star, we can use the law of conservation of energy. The initial potential energy of the object at the surface of the star is converted into kinetic energy as it falls.
Here are the steps to determine the velocity of the object:
Step 1: Find the gravitational potential energy (PE) at the surface of the neutron star.
The formula for gravitational potential energy is given by:
PE = mgh,
where m is the mass of the object, g is the gravitational acceleration, and h is the height.
In this case, the height is the distance it falls, given as 0.0086 m. The mass of the object is not provided, but we can assume it to be negligible compared to the neutron star's mass since it is falling near its surface.
Step 2: Use the law of conservation of energy to find the kinetic energy (KE) of the object.
The law of conservation of energy states that the total energy of a system remains constant. In this case, the initial potential energy is converted into kinetic energy.
The formula for kinetic energy is given by:
KE = 0.5 mv^2,
where m is the mass of the object and v is its velocity.
Since the mass of the object cancels out in this equation, we can calculate the velocity directly.
Step 3: Equate the gravitational potential energy to the kinetic energy.
Setting the gravitational potential energy equal to the kinetic energy, we have
PE = KE.
Step 4: Calculate the velocity.
Substituting the expressions for potential energy and kinetic energy, we get:
mgh = 0.5 mv^2.
Simplifying the equation, we find:
v^2 = 2gh.
Finally, we can solve for the velocity v.