Part A = 8.075 m/s

Part B = 0.255 m

What is his speed as he lands on the trampoline, 2.2 m below his jump off point?

If the trampoline behaves like a spring with spring stiffness constant 7.1 * 10^4 N/m , how far does he depress it? Any depression of the trampoline from equilibrium is to be taken as a negative distance.

Part A = d = mg/k + L

Part B = k = 2mgh / (h – L)^2

How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest?

If Kate just touches the surface of the river on her first downward trip (i.e., before the firstbounce), what is the spring constant k?

Part A = 1/2k((-L – x)^2 + (L – x)^2 + 2(-y)^2)

Part B = 2 * kxx(hat) + -2 * kyy(hat)

What is the potential energy of the two-spring system after the point of connection has been moved to position (x, y)?

Use the potential energy expression from Part A to find the force F on the junction point, the point where the two springs are attached to each other.

Part A = x_{2} = d / sqrt(2kH / mg)

Part B = x_{2} = (x_{1} * d) / (d – d_{12})

Two children are trying to shoot a marble of mass m into a small box using a spring-loaded gun that is fixed on a table and shoots horizontally from the edge of the table. The edge of the table is a height H above the top of the box (the height of which is negligibly small), and the center of the box is a distance d from the edge of the table. The spring has a spring constant k. The first child compresses the spring a distance x_{1} and finds that the marble falls short of its target by a horizontal distance d_{12}.

By what distance, x_{2}, should the second child compress the spring so that the marble lands in the middle of the box? (Assume that height of the box is negligible, so that there is no chance that the marble will hit the side of the box before it lands in the bottom.)

Now imagine that the second child does not know the mass of the marble, the height of the table above the floor, or the spring constant. Find an expression for x_{2} that depends only on X_{1} and distance measurements.

Part A = k = 2.5/0.005

Part B = 0.37 m

The following chart and accompanying graph depict an experiment to determine the spring constant for a baby bouncer.

What is the spring constant of the spring being tested for the baby bouncer?

One of the greatest difficulties with setting up the baby bouncer is determining the right height above the floor so that the child can push off and bounce. Knowledge of physics can be really helpful here.

If the spring constant k = 5.0 * 10^2 N, the baby has a mass m = 11 kg, and the baby’s legs reach a distance d = 0.15 m from the bouncer, what should be the height of the “empty” bouncer above the floor?

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