In the \"before\" part of the figure below, car A (mass 1000 kg) is stopped at a

Question

In the "before" part of the figure below, car A (mass 1000 kg) is stopped at a traffic light when it is rear-ended by car B (mass 1600 kg). Both cars then slide with locked wheels until the frictional force from the slick road (with a low µk of 0.14) stops them, at distances dA = 8.2 m and dB = 6.1 m.


(a) What is the speed of car A at the start of the sliding?
______m/s

(b) What is the speed of car B at the start of the sliding?
_______m/s

(c) Assuming that linear momentum is conserved during the collision, find the speed of car B just before the collision.
________m/s

(d) Explain why this assumption may be invalid.

Explanation / Answer

(a) if f is the frictional force then fromnewtons second law of motion we get f = m a the frictional force is given by f = µk n = µk mg the deceleration of each car will be a = f / m =µk m g / m =µk g if d is the stopping distance using the equationof motion we get the speed v of the car just after the impact as v2 = vo2 +2 a d as vo = 0 the speed of car A will be v2 = 2 a d vA = v(2 a d) = v(2µk g dA) = 4.7459m/s (b) the speed of car B will be vB = v(2 a d) = v(2µk g dB) = 4.09335m/s (c) if we take that v is the speed of car B just before the impact then from the law of conservation of linear momentum we get v = [(mA vA) +(mB vB)] / mB = 7.05955m/s

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.