A car and a truck carelessly approach an intersection and collide. The car and t

Question

A car and a truck carelessly approach an intersection and collide. The car and truck became so mangled that they stick together and their wheels lock up. Together they skid along the pavement to a stop. As physicists, you are called upon to help investigate what happened. At the scene, you see that the skid marks are 10 m long and are at an angle of 32 degrees north of west. You know a few things:

• The car was traveling west

•The truck was traveling north

• The truck is twice as massive as the car

• The coefficient of kinetic friction between rubber and asphalt is 0.67

• The wreck occurred in a 35 mph speed limit zone

Explanation / Answer

Considering mass of car is m then mass of truck will be 2m.

friction force on car and truck, f = uk N = uk (m + 2m)g = uk 3mg

so deceleration of system = f/M = uk 3m g / (m +2m) = uk g

a = - 0.67 x 9.8 = 6.57 m/s^2

using vf^2 - vi^2 = 2ad to find speed lockedup car truck just after collision.

0^2 - v^2 = 2(-6.57)(10)

v =11.46 m/s

suppose initial speed of car is Vc and initial speed of truck was Vt (just beforce collision)

Applying momentum conservation for collision,

m Vc(-i) + 2m Vt (j)   = (m + 2m) v (-cos32i + sin32j )

-Vc i + 2 Vt j = - 29.16 i + 18.22 j

so Vc = 29.16 m/s and Vt = 18.22 m/s

Speed of car = 29.16 x (1/1609) mile /(1/3600)hr = 65.24 mph

Speed of truck = 18.22 x (1/1609) mile /(1/3600)hr = 40.77 mph

so both truck and car were out of speed limit zone.

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