Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 7, Problem 68P

(a)

To determine

The velocity of the cars after the collision.

(a)

Expert Solution
Check Mark

Answer to Problem 68P

The velocity of the cars after the collision is 11m/s and the direction is 47° south of east.

Explanation of Solution

The mass of the car moving east ward is 1500kg, velocity of the car moving east ward is 17m/s, the mass of the car moving south ward is 1800kg and velocity of the car moving south ward is 15m/s.

Write the expression for the conservation of momentum in east direction.

mv=(m+M)vf

Here, vf is the final velocity of the cars in east direction, m is the mass of the car moving in east ward direction, M is the mass of the car moving south ward and v is the velocity of the car moving towards east.

Rewrite the above equation in terms of vf.

vf=mv(m+M). (I)

Write the expression for the conservation of momentum in south direction.

MV=(m+M)vf

Here, vf is the final velocity of the cars after collision in south direction and V is the velocity of the car moving south ward direction.

Rewrite the above equation in terms of vf.

vf=MV(m+M) (II)

Write the expression to calculate the final velocity of the cars.

Vf=vf2+(vf)2

Here, Vf is the final velocity of the cars.

Substitute (I) and (II) in the above equation to calculate Vf.

Vf=(mv(m+M))2+(MV(m+M))2=1m+M((mv)2+(MV)2)

Substitute 1500kg for m, 17m/s for v, 1800kg for M and 15m/s for V in the above equation to calculate Vf.

Vf=11500kg+1800kg((1500kg)2(17m/s)2+(1800kg)2(15m/s)2)=11.3m/s11m/s

Write the expression to calculate the direction of the final velocity of the cars.

ϕ=tan1(vfvf)

Here, ϕ is the direction.

Rewrite the above equation using (I) and (II).

ϕ=tan1(MVmv)

Substitute 1500kg for m, 17m/s for v, 1800kg for M and 15m/s for V in the above equation to calculate ϕ.

ϕ=tan1(1800kg(15m/s)1500kg(17m/s))=46.6°47°

Conclusion:

Therefore, The velocity of the cars after the collision is 11m/s and the direction is 47° south of east.

(b)

To determine

The amount of kinetic energy converted during the collision.

(b)

Expert Solution
Check Mark

Answer to Problem 68P

The amount of kinetic energy converted during the collision is 220kJ.

Explanation of Solution

Write the expression to calculate the amount of kinetic energy converted during collision.

ΔK=12(m+M)Vf212mv212MV2

Here, ΔK is the change in kinetic energy.

Substitute 1500kg for m, 17m/s for v, 1800kg for M, 11m/s for Vf and 15m/s for V in the above equation to calculate ΔK.

ΔK=12(1500kg+1800kg)(11m/s)212(1500kg)(17m/s)212(1800kg)(15m/s)2=199650J216750J202500J=219600J(1kJ1000J)220kJ

Thus, 220kJ of initial kinetic converted to another form of energy.

Conclusion:

Therefore, the amount of kinetic energy converted during the collision is 220kJ.

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Chapter 7 Solutions

Physics

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