A block of mass m slides down a frictionless incline as
The block is released from height h above the bottom of the circular loop.
(a) Find the force exerted on the block by the inclined track at point A. (Hint: Consider the Newton’s
2nd law in the radial direction and you may use polar coordinates for this circular part of the path to relate
the acceleration and velocity components.)
(b) Find the force exerted on the block by the inclined track at point B.
(c) Find the speed of the block at point B.
(d) What is the maximum height that the block can reach after leaving the track?
(e) Find the distance between point A and the point that the block land on ground level?
Did you get the answer to this?
To answer these questions, we need to consider the forces acting on the block at different points along its path.
(a) The force exerted on the block by the inclined track at point A can be determined using Newton's second law. In the radial direction, the only force acting on the block is the normal force. The normal force is perpendicular to the surface of the track and provides the necessary centripetal force to keep the block moving in a circular path.
(b) The force exerted on the block by the inclined track at point B is also the normal force, but its direction will be different since the block is now below the circular track. The normal force at point B will act towards the center of the circular loop.
(c) To find the speed of the block at point B, we need to use the conservation of energy. From point A to B, the block will lose potential energy but gain kinetic energy. By equating the change in potential energy to the gain in kinetic energy, we can solve for the speed.
(d) The maximum height that the block can reach after leaving the track can be determined by considering the conservation of mechanical energy. At the highest point, the block will have converted all its initial potential energy into kinetic energy. This can be used to find the maximum height.
(e) The distance between point A and the point where the block lands on the ground level can be calculated using the horizontal distance traveled by the block when it leaves the circular track. This can be found by considering the horizontal velocity of the block at that point and the time it takes to reach the ground.
To obtain the specific values and equations needed to solve these questions, more information about the geometry of the incline and circular track, as well as any initial conditions (such as the velocity of the block at point A), is required.