Finding the speed of a metal ball

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Homework Help Overview

The problem involves a metal ball of mass 0.500 kg rolling off a table and down a frictionless incline, with the goal of determining its speed just before it touches the floor. The context is rooted in energy conservation principles, specifically relating to potential and kinetic energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of energy conservation equations, questioning how to incorporate both potential energy and initial kinetic energy into their calculations. There is uncertainty about the effects of the frictionless incline on acceleration and how to account for the initial speed of the ball.

Discussion Status

Some participants have offered guidance on adjusting the energy equations to include initial kinetic energy. Multiple interpretations of how to approach the problem are being explored, particularly regarding the relationship between the ball's initial speed and its motion down the incline.

Contextual Notes

There is an emphasis on the frictionless nature of the incline and the initial conditions of the ball's motion, which may affect the assumptions made in the energy calculations.

smithers11
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alright, so here's my question that i have to answer:
"A ball of mass .500kg is rolling across a table top with a speed of 5.00 m/s. When the ball reaches the edge of the table, it rolls down a frictionless incline onto the floor 1.00 meter below (without bouncing). What is the speed of the ball when it reaches the floor (just before it touches the floor)?"

I use the equation PEf + KEf = PEi + KEi and then get KEf = PEi, which then leads to
.5mv^2 = mgh
From here, I'm stuck. Since the ramp is frictionless, does the ball accelerate the same as it would if it was dropped? And, how would I add in the initial speed of 5.00 m/s?
 
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smithers11 said:
I use the equation PEf + KEf = PEi + KEi and then get KEf = PEi, which then leads to
.5mv^2 = mgh
But KEi ≠ 0.
From here, I'm stuck. Since the ramp is frictionless, does the ball accelerate the same as it would if it was dropped?
No, it slides down the incline.
And, how would I add in the initial speed of 5.00 m/s?
That speed will be reflected in KEi.
 
ok so then i would change my equation to KEf = PEi + KEi, and then from there use the equation KEf = .5mv^2 to solve for the velocity (speed), right?
 
Right.
 

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