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Chapter 4: Problem 15

A truck driving on a level highway is acted on by the following forces: a downward gravitational force of \(52 \mathrm{kN}\) (kilonewtons); an upward contact force due to the road of \(52 \mathrm{kN} ;\) another contact force due to the road of \(7 \mathrm{kN},\) directed east; and a drag force due to air resistance of \(5 \mathrm{kN}\), directed west. What is the net force acting on the truck?

Short Answer

Expert verified
Answer: The net force acting on the truck is 2 kN in the eastward direction.

Step by step solution

01

Identify Horizontal and Vertical Components

To sum the forces vectorially, we need to split the four forces into horizontal and vertical components. Force 1: - Vertical component: \(52 \mathrm{kN}\) (downward) Force 2: - Vertical component: \(52 \mathrm{kN}\) (upward) Force 3: - Horizontal component: \(7 \mathrm{kN}\) (east) Force 4: - Horizontal component: \(5 \mathrm{kN}\) (west)
02

Calculate Net Vertical Force

To find the net vertical force (\(F_{v}\)), sum the vertical components of all four forces: \(F_{v} = -52 \mathrm{kN} + 52 \mathrm{kN} = 0 \mathrm{kN}\)
03

Calculate Net Horizontal Force

To find the net horizontal force (\(F_{h}\)), sum the horizontal components of all four forces: \(F_{h} = 7 \mathrm{kN} - 5 \mathrm{kN} = 2 \mathrm{kN}\)
04

Calculate the Net Force Acting on the Truck

Now we have the net horizontal force and the net vertical force, so we can calculate the net force (\(F_{net}\)) as follows: \(F_{net} = \sqrt{F_{v}^2 + F_{h}^2} = \sqrt{(0 \mathrm{kN})^2 + (2 \mathrm{kN})^2} = 2 \mathrm{kN}\) (east) The net force acting on the truck is \(2 \mathrm{kN}\) in the eastward direction.

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Most popular questions from this chapter

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