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. false true a 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? the speed of the cars after the collision is v/2. the total kinetic energy before and after the collision is conserved. this collision is completely inelastic. the total momentum before and after the collision is conserved.

Explanation:

First Question:

In an elastic collision, the total kinetic energy of the system (sum of kinetic energies of all objects in the system) is conserved. But the kinetic energy of each individual object can change. For example, in a one - dimensional elastic collision between two objects of different masses, the velocities (and thus kinetic energies) of the individual objects change while the total kinetic energy of the two - object system remains the same.

Step1: Apply conservation of momentum

The initial momentum is \(p_i = mv+0=mv\) (where \(m\) is the mass of the first car, \(v\) is its initial velocity and the second car has initial velocity \(u = 0\)). After the collision, the mass of the combined system is \(M=2m\) and let the final velocity be \(V\). By conservation of momentum \(p_i=p_f\), so \(mv=(m + m)V\). Solving for \(V\) gives \(V=\frac{v}{2}\).

Step2: Check kinetic energy conservation

The initial kinetic energy \(K_i=\frac{1}{2}mv^{2}+0=\frac{1}{2}mv^{2}\). The final kinetic energy \(K_f=\frac{1}{2}(2m)V^{2}\). Substitute \(V = \frac{v}{2}\) into \(K_f\), we get \(K_f=\frac{1}{2}(2m)(\frac{v}{2})^{2}=\frac{1}{4}mv^{2}\). Since \(K_i
eq K_f\), kinetic energy is not conserved.

Step3: Analyze collision type

Since the cars stick together, it is a completely inelastic collision. In any collision (elastic, inelastic, completely inelastic), momentum is conserved (assuming no external forces).

Answer:

A. False

Second Question: