a mass is at rest with respect to the lab frame, while a frictionless turntable rotates beneath it. the frequency of turntable is w and mass is located at radius r. In the frame of turntable , find the forces acting on mass and verify that F=ma
Calculate the weight of the following objects on earth (assume g=10N/kg) a)12kg b)500g c)20g d)what is the mass and weight of each of the objects if they were placed on mars? (g mars =3.8 N/kg)
To find the forces acting on the mass in the frame of the turntable, we need to consider two forces: the centrifugal force and the frictional force.
1. Centrifugal Force:
In the frame of the turntable, the mass appears to be moving in a circular path due to its rotation. According to Newton's first law of motion (inertia), an object at rest in the lab frame tends to remain at rest in the turntable frame. Therefore, a centrifugal force must act on the mass to keep it moving in the circular path.
The magnitude of the centrifugal force (F_c) can be calculated using the equation:
F_c = mω^2r,
where m is the mass, ω is the angular velocity (frequency) of the turntable, and r is the radius at which the mass is located.
2. Frictional Force:
Since the turntable is assumed to be frictionless, there is no frictional force acting on the mass in the frame of the turntable.
Now, to verify that F = ma, we need to consider the net force acting on the mass. In the frame of the turntable, the only force acting on the mass is the centrifugal force (F_c). According to Newton's second law of motion, the net force (F_net) is equal to the mass (m) times the acceleration (a):
F_net = ma.
Since the only force acting on the mass in the frame of the turntable is the centrifugal force, we can substitute F_c for F_net:
F = F_c = ma.
This verifies that F = ma in the frame of the turntable.
It's important to note that when analyzing forces in different frames of reference, we must include any fictitious forces in the non-inertial frame (like the centrifugal force in this case) to accurately account for the motion of objects.