5) One of my colleagues in grad school gave his lab students the following exper

Question

5) One of my colleagues in grad school gave his lab students the following experiment: A ball was rolled down a curving ramp from an initial height h. The ball then rolled across a horizontal section of the ramp, and shot o the end of the ramp with some horizontal speed v and initial height o the ground H. The ball would travel some horizontal distance x before hitting the ground. The idea behind the lab was that the students could use h and the mass m of the ball to find the initial potential energy, equate this initial energy mgh to the kinetic energy 1/2mv^2 of the ball as it left the table, and find v. From v and H, the students could then use projectile motion methods to predict exactly how far the ball would go before hitting the ground. The problem was that the ball consistently hit at about 85% of the “correct” distance. Air resistance and other non-conservative forces were not sucient to account for this discrepancy. (a) What was my colleague forgetting? Why was there this systematic error? (b) Show that a correct analysis gives an answer for x which is about 85% of the range predicted by the original analysis.

Explanation / Answer

(a) Your collegue was forgetting to take the friction between the ball and the ground into account.

Gravity is a conservative force which means that it is independent of the path taken. So it is the same for both the grounded motion and the projectile.

This is not the case for friction.

When the ball is thrown in a projectile, it is not subjected to frictional force whereas in the grounded motion it is present.

This accounts for the difference.

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