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Chapter 1: Problem 37

An object weighs \(20 \mathrm{lb}\) at a location where the acceleration of gravity is \(g=30.5 \mathrm{ft} / \mathrm{s}^{2}\). Determine the magnitude of the net force (lb) required to accelerate the object at \(25 \mathrm{ft} / \mathrm{s}^{2}\).

Short Answer

Expert verified
The net force (lb) required to accelerate the object at 25 ft/s^2 is given by the formula \(F = ma\). Hence, we need to first calculate the mass using the formula \(m = \frac{W}{g}\), and then substitute it into the net force formula.

Step by step solution

01

Calculate the Mass of the Object

The weight of an object can be found by using the equation \(W = mg\), where \(W\) is the weight, \(m\) is the mass, and \(g\) is the acceleration due to gravity. Here, we know that the weight of the object is 20 lb and the acceleration due to gravity is 30.5 ft/s^2. Therefore, you can solve for mass: \(m = \frac{W}{g} = \frac{20 \, \mathrm{lb}}{30.5 \, \mathrm{ft/s^2}}\).
02

Calculate the Required Net Force

The net force required to accelerate an object can be found using Newton's second law, \(F = ma\), where \(F\) is the net force, \(m\) is the mass, and \(a\) is the acceleration. Using the mass calculated in Step 1 and given acceleration \(a = 25 \, \mathrm{ft/s^2}\), the required net force is \(F = m \cdot a\).

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Most popular questions from this chapter

An incident occurred in which a cantilevered section of a walkway under demolition fell in a bagasse warehouse area at a sugar mill, resulting in the death of a worker positioned on top of the walkway. The incident walkway was constructed of two \(2.625\) in. by 10 in. steel C-channel main beams spaced three feet apart with metal floor grating welded to the top of the C-channel beams. The cantilevered walkway had welded-on hand rails and was approximately three \(\mathrm{ft}\) in width, \(11 \mathrm{ft}\) in length and located at a height of \(40 \mathrm{ft}\) from ground level. This section weighed more than \(800 \mathrm{lbs}\). The worker was positioned on the cantilevered portion of the walkway cutting through the floor grating of the walkway when the cantilevered walkway section unexpectedly gave way and fell to the area below. The demolition of the walkway left one section of the walkway cantilevered and supported by the metal floor grating and by an undersized weld. Demolition proceeded without an engineering study of the structural integrity of the bagasse walkway as well as an adequate plan for demolition. A proper engineering study of the structural integrity of the bagasse warehouse walkway as well as an adequate demolition plan in reasonable engineering probability would have prevented the accident. Search the OSHA regulation at http://www.osha.gov and review the sections 29 CFR 1926.501(a)(2) and 29 CFR 1926.850(a). Write a paragraph relating each section to the above incident and describe how following the regulations would have reduced the risk to employees.

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