a body of mass 1kg on the equator rotates about the axis of the earth with a period of 1 day. (mass of earth = 5.98x10^24kg n may b assumed to b concentrated at its centre n radius of earth = 6380km)
first question asks to calculate gravitational force of attraction between earth n mass....simple enuff
second qs asks to work out centripetal force on mass...easy
then it asks us to work out the difference between these two forces n use the answer as the resultant force to calucalte g at the equator using F =ma; what i've been taught is centripetal force is the resultant force so then y the need to find resultant force as the qs says. and then wat i also don't understand is why the resultant force is the difference between two forces that are acting in the same direction.
if someone cud clarify id b gr8ful
thanks in advance
The resultant force that they want is the modified force M g' that a scale would indicate for the object at the equator. It is less than the gravitational weight alone (M g) because
Gravity force - Indicated (scale) weight = Centripetal force
Therefore
Indicated weight = Gravity force - Centripetal force
g' = g - (V^2/R)
What you are really calculating is the resultant of the gravity force and the fictitious centriFUGAL force in the opposite direction.
A body of mass 1 kg is attracted by the earth with a force which is equal to :
In order to clarify your questions, let's break down the problem step by step:
1. Calculate the gravitational force of attraction between the Earth and the mass:
To calculate the gravitational force (F) between two objects, you can use Newton's law of universal gravitation:
F = (G * m₁ * m₂) / r²
where G is the gravitational constant (approximated as 6.67 x 10⁻¹¹ Nm²/kg²), m₁ is the mass of the Earth, m₂ is the mass of the body, and r is the distance between their centers of mass (approximated as the radius of the Earth).
2. Calculate the centripetal force on the mass:
The centripetal force (Fc) acting on an object moving in a circular path can be calculated using the formula:
Fc = m * v² / r
where m is the mass of the body, v is its velocity, and r is the radius (in this case, the radius of the Earth).
3. Find the difference between the gravitational force and the centripetal force:
To find the net force experienced by the mass, subtract the centripetal force from the gravitational force:
Resultant force (F) = Fg - Fc
4. Calculate g at the equator using F = m * a:
Since the net force (F) acting on the body can be defined as F = m * a, where m is the mass and a is the acceleration, you can rearrange the equation to solve for g:
g = F / m
Now, to address your confusion:
- The centripetal force is the resultant force, as it is responsible for keeping an object moving in a circular path. However, in this problem, the question asks for the net or resultant force by finding the difference between the gravitational force and the centripetal force. It wants to know the additional force that is required to keep the body rotating within the gravitational field.
- The resultant force is the difference between the two forces because they are acting in opposite directions. While the gravitational force pulls the mass towards the center of the Earth, the centripetal force pushes the mass outward due to its rotation. The difference between these two forces determines the net force experienced by the mass.
I hope this clarification helps!