A car with mass m_c = 1074\ kg is traveling west through an inte

Arthur Pratt 2021-12-19 Answered
A car with mass mc=1074 kg is traveling west through an intersection at a magnitude of velocity of vc = 15 m/s when a truck of mass mt=1593 kg traveling south at vt=10.8 ms fails to yield and collides with the car. The vehicles become stuck together and slide on the asphalt, which has a coefficient of friction of μk=0.5.
a)Write an expression for the velocity of the system after the collision, in terms of the variables given in the problem statement and the unit vectors i and j.
b)How far, in meters, will the vehicles slide after the collision?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Mary Herrera
Answered 2021-12-20 Author has 37 answers

Given information:
The mass of the car (mc)=1047 kg
The velocity of the car (vc)=15 ms=15 i ms (consider east as +ve x direction or +ve i)
The mass of the truck (mt)=1593 kg
The velocity of the truck (vt)=10.8 ms=10.8 j
According to law of conservation of momentum the momentum in all the direction is conserved, considering the along the "i" direction we can write:
mcvc+mtvt=(mc+mt)ViVi=(mcmc+mt)vc
Now, consider the momentum conservation along the "j" direction:
mcvc+mtvt=(mc+mt)VjVj=(mtmc+mt)vt
Therefore, the velocity of the vehicles after the collsion is:
V=(mcmc+mt)vci^(mtmc+mt)vtj^
By substituting the correspondingvalues, we get the velocity of the vehciles after the collision as:
V=6.04i^6.45j^|V|=8.836 ms
After the collision the cinetic energy of the both vehicles combined will be utilized to do work against the dricion force (given μk=0.5), The friction force both the vehicles is given by:
f=μk(mc+mt)g=0.5(1074+1593)9.81=13081.635 N
Now, according to work energy theorem the we can write:
12(mc+mt)V2=f.d
Where "d" is the distance travelled by the wreckage after the collision. Substituting the corresponding values, we get:
d=1074+15932(13081.635)×(8,836)2=7.958 m
Hence, the distance travelled by the wreckage after the collsion is 7.958 m.

Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-03-26
A pair of forces with equal magnitudes, opposite directions,and different lines of action is called a "couple". When acouple acts on a rigid object, the couple produces a torque thatdoes not depend on the location of the axis. The drawing shows acouple acting on a tire wrench, each force being perpendicular tothe wrench. Determine an expression for the torque produced by thecouple when the axis is perpendicular to the tired and passesthrough (a) point A, (b) point B, and (c) point C. Express youranswers in terms of the magnitude F of the force and the length Lof the wrench
asked 2021-02-12
The mechanics at lincoln automotive are reboring a 6-in deepcylinder to fit a new piston. The machine they are usingincreases the cylinder's radius one-thousandth of an inch every 3min. How rapidly is the cylinder volume increasing when thebore(diameter) is 3.800 in
asked 2021-04-15

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors i^ and j^.
1. (Enter in box 1) ms2i^+( Enter in box 2 )ms2j^
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) ms2i^+
5. ( Enter in box 5) ms2j^

asked 2020-11-23
Saturn has an equatorial radius of 6.00 107 mand a mass of 5.67 1026 kg.
(a) Compute the acceleration of gravity at the equatorof Saturn.
(b) What it the ratio of a person's weight on Saturn to that onEarth?
asked 2022-01-05
A 5.80μF, parallel-plate, air capacitor has a plate separation of 5.00 mm and is charged to a potential difference of 400 V. Calculate the energy density in the region between the plates, in units of Jm3.
asked 2021-11-07
Suppose you have 1.0 mol of O2 gas. How many coulombs of positive charge are contained in the atomic nuclei of this gas?
asked 2022-08-28

(x-5) (x+5)

 

 

New questions

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question