Mastering Physics Solutions: Hooke’s Law

Mastering Physics Solutions: Hooke’s Law

On December 20, 2011, in Chapter 05: Work and Energy, by Mastering Physics Solutions

Hooke’s Law (± Hooke’s Law or Hookes Law)

Part A = k = 4.0*104 N/m Click to use the calculator/solver for this part of the problem
Part B = x = 0.45m Click to use the calculator/solver for this part of the problem
Part C = No, typical small pickup truck springs are not large enough to compress 0.45 m.
Part D = The new springs should have a spring constant that is substantially larger than the spring constant of the old springs.

Solutions Below:

In Haiti, public transportation is often by taptaps, small pickup trucks with seats along the sides of the pickup bed and railings to which passengers can hang on. Typically they carry two dozen or more passengers plus an assortment of chickens, goats, luggage, etc. Putting this much into the back of a pickup truck puts quite a large load on the truck springs.

A truck has springs for each wheel, but for simplicity assume that the individual springs can be treated as one spring with a spring constant that includes the effect of all the springs. Also for simplicity, assume that all four springs compress equally when weight is added to the truck and that the equilibrium length of the springs is the length they have when they support the load of an empty truck.

Part A

A 65 kg driver gets into an empty taptap to start the day’s work. The springs compress 1.6*10-2 m. What is the effective spring constant of the spring system in the taptap?

We know that F = kx. Therefore:

65kg * g = -k(1.6*10-2)
-637N = -0.016k (the force is negative because gravity is downward)
k = 39,812,5

And to 2 significant figures:

k = 4.0*104 N/m

Part B

After driving a portion of the route, the taptap is fully loaded with a total of 27 people including the driver, with an average mass of 65 kg per person. In addition, there are three 15 kg goats, five 3 kg chickens, and a total of 25 kg of bananas on their way to the market. Assume that the springs have somehow not yet compressed to their maximum amount. How much are the springs compressed?

First, solve for the total mass loaded onto the taptap:

m = (27 * 65) + (3 * 15) + (5 * 3) + 25
m = 1,840kg

And the gravitational force (the weight of everything loaded in the taptap) is:

F = ma
F = 1,840*9.8
F = -18,032 N (negative because the force is downward)

Using the k that we found in Part A, solve for x:

F = -kx
-18,032 = -4.0*104x

x = 0.45m

Part C

Whenever you work a physics problem you should get into the habit of thinking about whether the answer is physically realistic. Think about how far off the ground a typical small truck is. Is the answer to Part B physically realistic?

The answer is no. At least according to Mastering Physics:

No, typical small pickup truck springs are not large enough to compress 0.45 m.

Part D

Now imagine that you are a Haitian taptap driver and want a more comfortable ride. You decide to replace the springs with new springs that can handle the typical heavy load on your vehicle. What spring constant do you want your new spring system to have?

New, stronger springs will compress less. So the spring constant k will have to be greater:

The new springs should have a spring constant that is substantially larger than the spring constant of the old springs.

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2 Responses to Mastering Physics Solutions: Hooke’s Law

  1. Gustavo Gomez says:

    For Part A, the power of 10 is supposed to be: 10^4 N/m

    • Mastering Physics Solutions says:

      Yes indeed- the calculator figured it correctly but the written answer was wrong. Thanks for the correction!

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