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If a car generates 18 hp when traveling at a steady what must be the average force exerted on the car due to friction and air resistance?

Short Answer

Expert verified

The average force exerted on the car due to friction and air resistance is 508.64 N.

Step by step solution

01

Identification of the given data

The power generated by the car engine is\(P = 18\;{\rm{hp}} \times \frac{{746\;{\rm{W}}}}{{1\;{\rm{hp}}}} = 13428\;{\rm{W}}\).

The steady speed of the car is \(v = 95\;{\rm{km/h}} \times \frac{{1\;{\rm{m/s}}}}{{3.6\;{\rm{km/h}}}} = 26.4\;{\rm{m/s}}\).

02

Definition of power

Power, P is defined as the rate at which work is done and is obtained by dividing the time taken to perform that work. It is given as:

\(P = \frac{W}{t}\)... (i)

03

Relationship between power and force

The average power in terms of force can be written as:

\(\begin{aligned}{P_{{\rm{av}}}} &= \frac{{{\rm{Work}}}}{{{\rm{time}}}}\\ &= \frac{{{\rm{Force}} \times {\rm{distance}}}}{{{\rm{time}}}}\\ &= {\rm{Force}} \times {\rm{speed}}\\ &= Fv\end{aligned}\) … (ii)

Here, the force and speed are in the same direction.

04

Determination of average force exerted by the car

The power generated by the engine creates a force on the ground to propel the car in the forward direction.

Thus, the force required to propel the car in the forward direction is given by equation (ii). It is given that the car moves with a steady velocity.The resistive force is of the same magnitude as the engine force, and so the net force is zero.

Thus, the average force exerted on the car due to friction and air resistance is given by equation (ii).

\(\begin{aligned}F &= \frac{{{P_{{\rm{av}}}}}}{v}\\ &= \frac{{13428\;{\rm{W}}}}{{26.4\;{\rm{m/s}}}}\\ &= 508.64\;{\rm{N}}\end{aligned}\)

Thus, the resistive force is 508.64 N.

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Most popular questions from this chapter

You lift a heavy book from a table to a high shelf. List the forces on the book during this process, and state whether each is conservative or nonconservative.

Consider a force \(F{\bf{ = 80}}\;{\bf{N}}\) applied to a beam as shown in Fig. 8–37. The length of the beam is \(l{\bf{ = 5}}{\bf{.0}}\;{\bf{m}}\) and \(\theta {\bf{ = 3}}{{\bf{7}}^{\bf{o}}}\), so that \(x{\bf{ = 3}}{\bf{.0}}\;{\bf{m}}\) and \(y{\bf{ = 4}}{\bf{.0}}\;{\bf{m}}\). Of the following expressions, which ones give the correct torque produced by the force around point P?

(a) 80 N.

(b) (80 N)(5.0 m).

(c) (80 N)(5.0 m)(sin 37°).

(d) (80 N)(4.0 m).

(e) (80 N)(3.0 m).

(f) (48 N)(5.0 m).

(g) (48 N)(4.0 m)(sin 37°).

FIGURE 8-37MisConceptual Question 5.

List some everyday forces that are not conservative, and explain why they aren’t.

You push very hard on a heavy desk, trying to move it. You do work on the desk:

(a) whether or not it moves, as long as you are exerting a force.

(b) only if it starts moving.

(c) only if it doesn’t move.

(d) never—it does work on you.

(e) None of the above.

Two blocks of mass\({m_{\rm{A}}}\)and\({m_{\rm{B}}}\), resting on a frictionless table, are connected by a stretched spring and then released (Fig. 7–48). (a) Is there a net external force on the system before release? (b) Determine the ratio of their speeds,\({v_{\rm{A}}}/{v_{\rm{B}}}\)(c) What is the ratio of their kinetic energies? (d) Describe the motion of the CM of this system. Ignore mass of spring.

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