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Answer :
The force on the mass when it is located at r = 6.38×10⁶ m is approximately 97.8 N away from the reference point.
The potential energy of a mass can be calculated using the equation:
Potential energy = -3.98×10¹⁵ / r
where r represents the distance of the mass from its reference point.
In this case, the mass is 10 kg and the potential energy is given as -3.98×10¹⁵ / r.
To find the force on the mass when it is located at r = 6.38×10⁶ m, we need to take the derivative of the potential energy equation with respect to r:
Force = d(Potential energy) / d(r)
To calculate the derivative, we treat the -3.98×10¹⁵ as a constant:
Force = (-3.98×10¹⁵) * d(1/r) / d(r)
The derivative of 1/r with respect to r is -1/r²:
Force = (-3.98×10¹⁵) * (-1/r²)
Simplifying the expression, we get:
Force = (3.98×10¹⁵) / r²
Now we can substitute the value of r = 6.38×10^6 m into the equation to find the force:
Force = (3.98×10¹⁵) / (6.38×10⁶)²
Calculating this, we get:
Force ≈ 97.8 N away from r=0
Therefore, the force on the mass when it is located at r = 6.38×10⁶ m is approximately 97.8 N away from the reference point.
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