As shown in Figure 2.12. a ball with mass m is propelled by a spring with a spri
ID: 2991481 • Letter: A
Question
As shown in Figure 2.12. a ball with mass m is propelled by a spring with a spring stiffness k to roll without friction on a surface until it is launched into the air by a ramp of height h The departure angle 7 is fixed by the ramp and is not a variable The goal is to hit a target on ground level a distance d away from the ramp Find the initial velocity v0 the ball must have when leaving the ramp to hit the target What is the initial compression ; the spring must have such that the mass will haw the necessary velocity t0 when leaving the ramp?Explanation / Answer
(a) For projectile motion, we have
d = v0 (Cos )/g (v0 Sin + ((v0 Sin )2 + 2gh)0.5)
This equation gives the relation for v0 in terms of known quantities.
(b) Energy stored in spring = 1/2*kz2.
Total energy (KE + PE) at the time of leaving the ramp = mgh + 1/2*mv02.
Equating both and solving for z, we get z = [2/k*(mgh + 1/2*mv02)]0.5
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