A new event has been proposed for the Winter Olympics. An athlete will sprint 10

Question

A new event has been proposed for the Winter Olympics. An athlete will sprint 100 m, starting from rest, then leap onto a 19kg bobsled. The person and bobsled will then slide down a 48-m-long ice-covered ramp, sloped at 20 degree . and into a spring with a carefully calibrated spring constant of 1600N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 45kg, has been training for this event. She can reach a maximum speed of 12m/s in the 100 m dash. (Figure 1) How far will Lisa compress the spring? Express your answer to two significant figures and include the appropriate units. The Olympic committee has very exact specifications about the shape and angle of the ramp. Is this necessary? What factors about the ramp are important? answers are limited to about 500 words (3800 characters

Explanation / Answer

First we need to find the speed of Lisa and the bobsled as soon as she jumps on. This can be considered a completely inelastic collision, since she stays on the bobsled. Use the conservation of momentum equation:
m1v1i + m2v2i = (m1 + m2)vf
(45 kg)(12 m/s) + (19 kg)(0 m/s) = (45 + 19 kg)vf
vf = 8.43 m/s

Now we can find how much Lisa and the bobsled will compress the spring. This problem is easiest to solve using conservation of energy with springs:
(KE + PEg + PEs)i = (KE + PEg + PEs)f
We can cross out PEsi, KEf, and PEgf because those are zero.
KEi + PEgi = PEsf
1/2 mv^2 + mgh = 1/2 kx^2
sin(20

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.