A new game, PhysicsPong^, has been invented. The goal is to fire a mass into a c

Question

A new game, PhysicsPong^, has been invented. The goal is to fire a mass into a cup. Your job is to compress a spring, and then release the mass. The mass is fired off the end of the horizontal table, and - if you did your calculations correctly! - into a cup that is on the floor. In this variation we have a 0.3 kg mass aiming at a cup that is 3.5 meters from the end of the table. Our spring has a spring constant of 50 N/m. A point A is labelled, but there is nothing there. Treat the table as frictionless. Diagram is not to scale (the mass would not fit in the cup if it were to scale!) (a) How fast would the mass have to be travelling at the end of the table (i.e. the point marked "A") for it to land in the cup? (b) How much would we have to compress the spring so that the cup would land in the cup?

Explanation / Answer

Given horizontal distance s = 3.5 m

vetical height y =b1.8 m

let t be the time to reach from point A to the cup

we have

y = v0y * t + (1/2 * g * t^2)

here v0y = 0 (initial vertical velocity so

y = n1/2 * g * t^2

1.8 = 1/2 * 9.8 * t^2

therefore t = 0.606 s

now horizontal distance s = v0 * t (no horizontal acceleration)

3.5 = v0 * 0.606

v0 = 5.77 m/s

part b)

from conservation of energy

elastic energy = kinetic energy

1/2 * k * x^2 = 1/2 * m * v^2

1/2 * 50 * x^2 = 1/2 * 0.3 * 5.77^2

compreesed length x = 0.45 m

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