A spring has an unstretched length of 12 cm. It exerts a restoring force F when

Question

A spring has an unstretched length of 12 cm. It exerts a restoring force F when stretched to a length of 14 cm. For what length of the spring is its restoring force 3^F? Express your answer to two significant figures and include the appropriate units. At what compressed length is the restoring force 2^F? Express your answer to one significant figure and include the appropriate units. A new event has been proposed for the Winter Olympics. An athlete will sprint 100 m, starting from rest, then leap onto a 23 kg bobsled. The person and bobsled will then slide down a 49-m-long ice-covered ramp, sloped at 20 degree, and into a spring with a carefully calibrated spring constant of 2500 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 42 kg, has been training for this event. She can reach a maximum speed of 12 m/s in the 100 m dash. 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?

Explanation / Answer

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10.8

a)

the restoring fore is directly proprtional to strectchedlength.

so,

F2/F1=l2/l1

      l2=(F2/F1)l1

          =(3F/F)(2 cm)

         = 6 cm

(b)

F2/F1=l2/l1

      l2=(F2/F1)l1

          =(2F/F)(2 cm)

          = 4 cm

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