What Is the Car's Speed After Exiting the Mud Patch?

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Homework Help Overview

The problem involves a car with a mass of 1100 kg traveling at an initial speed of 24 m/s that encounters a mud patch with a resistive force. The objective is to determine the car's speed after exiting the mud patch, considering the effects of the resistive force over a distance of 18 m.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between kinetic energy and work done by the resistive force. There is uncertainty about how to incorporate initial kinetic energy and the work done by the resistive force into the calculations. Some participants express doubt about the accuracy of initial calculations and suggest that the resistive force would significantly reduce the car's speed.

Discussion Status

Participants are exploring different interpretations of the problem, with some suggesting that the initial kinetic energy must be accounted for in the calculations. There is acknowledgment of the need to reconsider the approach to the problem, and one participant has indicated a revised speed that seems more reasonable.

Contextual Notes

There is a mention of potential errors in calculations and the need to clarify the relationship between initial kinetic energy and the work done by the resistive force. The discussion reflects a collaborative effort to refine understanding and approach to the problem.

alison16
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Homework Statement


A 1100kg car is traveling at 24m/s before it hits a 18m patch of mud with a 1.7 x 10^4 net horizontal resistive force. What is the cars speed as it leaves the mud patch?

Homework Equations


Change in Uint= fd
KE= 1/2mv^2
W= Fd

The Attempt at a Solution


1/2mv^2 = f(mud on car)d
1/2(1100)v^2 = 1.7 x 10^4(18)
V= 23.6 m/s

I'm pretty sure this isn't correct, because the resistive force is too great to have the final velocity change only slightly. I feel like I might need to incorporate work or the initial velocity into my equation, but I don't really know how.
 
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alison16 said:

Homework Statement


A 1100kg car is traveling at 24m/s before it hits a 18m patch of mud with a 1.7 x 10^4 net horizontal resistive force. What is the cars speed as it leaves the mud patch?

Homework Equations


Change in Uint= fd
KE= 1/2mv^2
W= Fd

The Attempt at a Solution


1/2mv^2 = f(mud on car)d
1/2(1100)v^2 = 1.7 x 10^4(18)
V= 23.6 m/s

I'm pretty sure this isn't correct, because the resistive force is too great to have the final velocity change only slightly. I feel like I might need to incorporate work or the initial velocity into my equation, but I don't really know how.

The car starts out with some initial KE due to its initial velocity. The friction "robs" energy from this initial store of KE. So find out how much KE is left after traversing the mud patch...
 
Must be the battery in the calculator. Left and right are both of the order of 300000 J so there must be a considerable slowdown.
Means your intuition is good. Both work (from resistive force) and inital velocity (*) are in your equation (assuming your KE means ΔKE), which is just fine. Some typo on the calculator ?

[edit] (*) realize I misinterpreted what you wrote. As gneill (the doctor) says: ΔKE instead of ½mv2 and you're fine.
 
Last edited:
Got it! 4.4 m/s is much more resonable. Thank you.
 

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