laws- of- motion problem

In summary, two particles of the same mass and size are released simultaneously from one end of a diameter of a hemispherical surface, one along a wire joining the diameter and one along the hemispherical surface. The surface is frictionless and the wire has no tension. Both particles have a horizontal velocity of v. The particle traveling along the hemisphere reaches the other end first due to the force present along the surface, causing its speed to gradually rise and then decrease by the conservation of energy principle. Despite having a longer path, the increase in speed compensates for this and allows the particle to reach the end first. There is no mathematical explanation given for the force along the hemisphere.
  • #1
physixguru
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Two particles of same mass and size are released SIMULTANEOUSLY from one end of a diameter of a hemispherical surface, along a wire joining the diameter and along the hemispherical surface respectively..The hemispherical surface is frictionless AND WIRE HAS NO TENSION..Both have a horizontal velocity v.

WHICH REACHES THE OTHER END FIRST?
 
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  • #2
The speed of the particle on the hemisphere gradually rises because of the force present along the hemisphere surface.And once it has reached the bottom most point its speed decreases gradually and becomes v again by conservation of energy principle.So even though the path of the body traveling along the hemisphere is more but the speed increase more than makes up for it.And hence particle going along the hemisphere reaches first.

I don't have any mathematical explanation.Srry.
 
  • #3
what force along the " hemisphere"?
 

What is Newton's First Law of Motion?

Newton's First Law of Motion states that an object will stay at rest or continue moving in a straight line at a constant velocity unless acted upon by an external force.

What is Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This can be represented by the equation F=ma, where F is the net force, m is the mass of the object, and a is the acceleration.

What is Newton's Third Law of Motion?

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force on the first object.

How do I solve a "laws-of-motion problem"?

To solve a "laws-of-motion problem", you must first identify all the forces acting on the object and their directions. Then, use Newton's Second Law of Motion to calculate the net force on the object. Finally, use this net force to calculate the object's acceleration and solve for the unknown variable.

What are some real-life examples of Newton's Laws of Motion?

Some real-life examples of Newton's Laws of Motion include a person pushing a shopping cart (First Law), a rocket taking off into space (Second and Third Law), and a person jumping off a diving board (Third Law).

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