Calculate the difference between the magnitude of the gravitational force and the magnitude of the normal force exerted on a 100 kg object at the equator. Which of the two forces is equal in magnitude to the weight of the object?
The "normal force" is the measured weight.
Gravitational force MINUS weight equals the centripetal force, M V^2/R
where R is the radius of the Earth and V is the Earth rotational velocity at the equator, 464 m/s
For a 100 kg object, the difference is
100*(464)^2/6380*10^3 = 3.8 N
which is about 0.85 pound.
To calculate the difference between the magnitude of the gravitational force and the magnitude of the normal force exerted on a 100 kg object at the equator, we need to understand the forces involved.
1. Gravitational Force:
The gravitational force experienced by an object is given by the equation:
F_gravity = m * g
where F_gravity is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity. On the Earth's surface, the value of g is approximately 9.8 m/s^2.
2. Normal Force:
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, when the object is at the equator, the normal force will be equal in magnitude but opposite in direction to the gravitational force.
To calculate the magnitude of the normal force, we can use the equation:
F_normal = m * g
where F_normal is the magnitude of the normal force.
3. The Weight of the Object:
The weight of an object is equal to the magnitude of the gravitational force acting on it. Therefore, the weight of a 100 kg object can be calculated using the equation:
Weight = m * g
where Weight is the magnitude of the weight of the object.
Now, to find the difference between the magnitude of the gravitational force and the magnitude of the normal force, we can simply subtract the magnitude of the normal force from the magnitude of the gravitational force:
Difference = |F_gravity - F_normal|
To summarize,
- Calculate the gravitational force using the equation F_gravity = m * g, where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2).
- Calculate the normal force using the equation F_normal = m * g.
- Calculate the weight of the object using the equation Weight = m * g.
- Find the difference between the gravitational force and the normal force using the equation Difference = |F_gravity - F_normal|.
- The force that is equal in magnitude to the weight of the object is the gravitational force.