1.A new event has been proposed for the Winter Olympics. An athlete will sprint
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Question
1.A new event has been proposed for the Winter Olympics. An athlete will sprint 100 m, starting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 50-m-long ice-covered ramp, sloped at 20 degree , and into a spring with a carefully calibrated spring constant of 2000 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40 kg, has been training for this event. She can reach a maximum speed of 12 m/s in the 100 m dash.
question-How far x will Lisa compress the spring? in m
2.A spring-loaded toy gun is used to shoot a ball of mass 1.50 kg straight up in the air, as shown in the figure. The spring has spring constant 667N/m. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y=0 and then released, the ball reaches a maximum height h maximum(measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y axis.
question a.Find v the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position y=0 ).in m/s
b-Find the maximum height of the ball.in m
Explanation / Answer
use the Hooke's law 1. I would use the energy conservation. So do this by parts. 0.5mv^2+(m+m1)(g)(sin 20)(h)=0.5kx^2 m is lisa's mass m1 is the bobsled. g is gravity. h is length of the ramp. The first term where there is no m1, is because its teh energy of lisa runnning to the sled. And then she comes down with the sled, so u combine both mass, times gravity, times the height. To find the actual height, u just use simple trig 50sin 20 is ur actual height. All that energy will be used in compressing teh spring, which is 0.5kx^2 k is teh sprign constant, x is how much it compresses. Solve for x. You get 3.59658062800971 meters.
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