Question

to answer this question, first click here to view the associated video.true or false: in an elastic collision, the kinetic energy of each object is the same both before and after the collision.falsetruea car of mass m moving with a speed v collides with an identical car that is at rest. after the collision, the cars stick together.which of the following statements is false?this collision is completely inelastic.the total momentum before and after the collision is conserved.the total kinetic energy before and after the collision is conserved.the speed of the cars after the collision is v/2.

Explanation:

First Question:

Step1: Recall elastic collision definition

In an elastic collision, total kinetic energy is conserved, not kinetic energy of each object. For example, a moving object colliding elastically with a stationary one: the first object may slow down and the second speed up. So kinetic energy of each object changes.

Second Question:

Step1: Analyze collision type

Since cars stick together, it's a completely inelastic collision.

Step2: Check momentum conservation

In any collision (isolated system), total momentum is conserved. Using \(p = mv\), initial momentum \(p_i=mv + m\times0=mv\), final momentum \(p_f=(m + m)v_f\). By \(p_i = p_f\), \(mv=(2m)v_f\), so \(v_f=\frac{v}{2}\).

Step3: Check kinetic energy conservation

Initial kinetic energy \(K_i=\frac{1}{2}mv^2+0=\frac{1}{2}mv^2\). Final kinetic energy \(K_f=\frac{1}{2}(2m)(\frac{v}{2})^2=\frac{1}{4}mv^2\). So total kinetic energy is not conserved.

Answer:

First Question: A. False
Second Question: C. The total kinetic energy before and after the collision is conserved.