Impulse and Momentum: Find Common Velocity & Fraction of Kinetic Energy

In summary: J/111,600J = .000005. In summary, the two cars, weighing 1550kg and 1220kg respectively, collide with a velocity of 12m/s and lock bumpers, resulting in a shared velocity of 6.71m/s. The fraction of initial kinetic energy that remains after the collision is approximately 0.000005.
  • #1
rmarkatos
33
0
A 1550kg car, traveling with a velocity of 12m/s plows into a 1220kg stationary car. During the collision the two cars lock bumpers and then move together as a unit. (a) what is tehir common velocity just after the impact?
(b) What fraction of the initial kinetic energy remains after the collision.

(a) Pf=Pi

(m1+m2)vf=m1vi1
(1550kg+1220kg)vf=1550kg(12m/s)
2770kgvf=18600kg m/s

vf=6.71 m/s
I know my answer for part A is correct but part B i really have no idea how to approach it.
 
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  • #2
rmarkatos said:
A 1550kg car, traveling with a velocity of 12m/s plows into a 1220kg stationary car. During the collision the two cars lock bumpers and then move together as a unit. (a) what is tehir common velocity just after the impact?
(b) What fraction of the initial kinetic energy remains after the collision.

(a) Pf=Pi

(m1+m2)vf=m1vi1
(1550kg+1220kg)vf=1550kg(12m/s)
2770kgvf=18600kg m/s

vf=6.71 m/s
I know my answer for part A is correct but part B i really have no idea how to approach it.
What is the initial kinetic energy of the system just before impact? What is the kinetic energy of the system immediately after impact? What is the ratio of the 2 values?
 
  • #3
would the kinetic energy of the system just be the kinetic energy of the object the first car since the second one was stationary.

By the way the answer to the question is .559J from the odd selected answer section but i am not sure how to get the answer

ke=1/2mv^2
(1/2)(1550kg)(12m/s)^2
ke=111,600J

would the kinetic energy after be the sum of masses of the 2 cars with the shared final velocity?

ke=1/2mv^2
=(1/2)(2770kg)(6.71m/s)^2
=62358J the difference is not equal to .559J
 
  • #4
rmarkatos said:
would the kinetic energy of the system just be the kinetic energy of the object the first car since the second one was stationary.

By the way the answer to the question is .559J from the odd selected answer section but i am not sure how to get the answer

ke=1/2mv^2
(1/2)(1550kg)(12m/s)^2
ke=111,600J

would the kinetic energy after be the sum of masses of the 2 cars with the shared final velocity?

ke=1/2mv^2
=(1/2)(2770kg)(6.71m/s)^2
=62358J the difference is not equal to .559J
Your calcs are correct, but they did not ask for the difference, they asked for the fraction of initial energy left. KE_f/KE_i = ??
 
  • #5
ohhhhh your right thanks for clearing that up for me that makes a big difference
 

FAQ: Impulse and Momentum: Find Common Velocity & Fraction of Kinetic Energy

1. What is impulse and momentum?

Impulse and momentum are two closely related concepts in physics. Momentum is a measure of an object's motion, determined by its mass and velocity. Impulse, on the other hand, is a change in an object's momentum caused by a force acting on it for a certain amount of time.

2. How do you calculate impulse?

Impulse is calculated as the force applied to an object multiplied by the time interval over which it acts. This can be represented by the equation I = FΔt, where I is impulse, F is force, and Δt is the change in time.

3. What is the relationship between impulse and momentum?

Impulse and momentum are directly proportional to each other. This means that a larger impulse will result in a larger change in momentum, and vice versa. In other words, the greater the force and/or the longer the time interval, the greater the change in momentum.

4. How do you find the common velocity in a collision?

In a collision between two objects, the common velocity is the final velocity that both objects will have after the collision. It can be found by dividing the total momentum of the system by the total mass of the system. This can be represented by the equation v = P/m, where v is the common velocity, P is the total momentum, and m is the total mass.

5. How do you calculate the fraction of kinetic energy after a collision?

The fraction of kinetic energy after a collision can be calculated by dividing the kinetic energy of the system after the collision by the initial kinetic energy of the system before the collision. This can be represented by the equation KEf/KEi, where KEf is the final kinetic energy and KEi is the initial kinetic energy.

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