Answer :
The radius of curvature of the surface can be calculated using the given information of the normal force and the mass of the sack.
Here's the step-by-step explanation:
1) The normal force (N) acting on the sack is equal to the weight of the sack (W) when the sack is at rest or moving at a constant speed on a flat surface.
This can be represented by the equation N = W.
2) The weight (W) of the sack can be calculated using the formula W = mg, where m is the mass of the sack and g is the acceleration due to gravity (approximately 9.81 m/s^2).
3) Since the mass of the sack is given as 10 kg, its weight can be calculated as W = 10 kg x 9.81 m/s^2 = 98.1 N.
4) At the flat spot on the surface, the normal force is equal to the weight of the sack, which is given as 98.1 N.
5) As the sack slides down the surface, it will experience a centrifugal force due to the curved surface.
The magnitude of the centrifugal force can be calculated using the formula Fc = mv^2/r, where m is the mass of the sack, v is the velocity of the sack, and r is the radius of curvature of the surface.
6) Since the surface is smooth, there is no frictional force acting on the sack.
7) At the flat spot, the velocity of the sack is zero. As it slides down the surface, its velocity will increase.
8) When the sack reaches the curved portion of the surface, it will experience a centrifugal force that is equal in magnitude to the force of gravity (i.e., the weight of the sack).
9) Using the formula Fc = mv^2/r, and substituting the values of m, v, and Fc with the weight of the sack, the velocity of the sack can be calculated.
10) Once the velocity is known, the radius of curvature can be calculated using the formula r = mv^2/Fc.
11) Therefore, the radius of curvature of the surface can be calculated by substituting the values of m, v, and Fc with the weight of the sack and the given normal force (N = 98.1 N).
The radius of curvature can be calculated as r = (m x g)/(N/m) = (10 kg x 9.81 m/s^2)/(98.1 N/10 kg) = 1.0 meters.
In summary, the radius of curvature of the surface can be calculated as 1.0 meters, given that the normal force at the flat spot on the surface is 98.1 N and the mass of the sack is 10 kg.
To know more about Normal force refer here :
https://brainly.com/question/18799790
#SPJ11
