Mastering Physics Solutions: Problem 6.37

Mastering Physics Solutions: Problem 6.37

On March 16, 2014, in Chapter 05: Work and Energy, by Mastering Physics Solutions

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.

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Mastering Physics Solutions: Bungee Jumping

Mastering Physics Solutions: Bungee Jumping

On October 11, 2013, in Chapter 05: Work and Energy, by Mastering Physics Solutions

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?

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Mastering Physics Solutions: Springs in Two Dimensions

Mastering Physics Solutions: Springs in Two Dimensions

On October 2, 2013, in Chapter 05: Work and Energy, by Mastering Physics Solutions

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.

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Mastering Physics Solutions: Shooting a ball into a box

Mastering Physics Solutions: Shooting a ball into a box

On February 23, 2013, in Chapter 05: Work and Energy, by Mastering Physics Solutions

Part A = x2 = d / sqrt(2kH / mg)
Part B = x2 = (x1 * d) / (d – d12)

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 x1 and finds that the marble falls short of its target by a horizontal distance d12.

By what distance, x2, 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 x2 that depends only on X1 and distance measurements.

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Mastering Physics Solutions: Baby Bounce with a Hooke

Mastering Physics Solutions: Baby Bounce with a Hooke

On February 22, 2013, in Chapter 05: Work and Energy, by Mastering Physics Solutions

Part A = k = 2.5/0.005
Part B = 0.37 m Click to use the calculator/solver for this part of the problem

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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