### Learning Objectives

Define inelastic collision.Explain perfectly inelastic collision.Apply an knowledge of collisions to sports.Determine recoil velocity and loss in kinetic power given mass and initial velocity.You are watching: Is mechanical energy conserved in an inelastic collision

We have seen that in one elastic collision, interior kinetic energy is conserved. An inelastic collision is one in i beg your pardon the interior kinetic energy transforms (it is no conserved). This lack of conservation way that the forces between colliding objects may remove or add internal kinetic energy. Work-related done by internal pressures may change the forms of power within a system. For inelastic collisions, together as when colliding objects stick together, this internal work may transform some internal kinetic energy into heat transfer. Or the may convert stored power into internal kinetic energy, together as as soon as exploding bolts separate a satellite from its start vehicle.

Inelastic Collision

An inelastic collision is one in which the interior kinetic energy changes (it is no conserved).

(Figure) shows an instance of an inelastic collision. 2 objects that have equal masses head towards one one more at equal speeds and also then rod together. Their full internal kinetic energy is at first

Strategy

Momentum is conserved since the net exterior force top top the puck-goalie mechanism is zero. We have the right to thus use conservation of inert to find the final velocity of the puck and goalie system. Keep in mind that the initial velocity of the goalie is zero and also that the last velocity of the puck and also goalie are the same. Once the final velocity is found, the kinetic energies can be calculate before and after the collision and compared as requested.

**Solution because that (a)**

Momentum is conserved because the net outside force on the puck-goalie system is zero.

Conservation of inert is

or

Because the goalie is at first at rest, we understand

. Because the goalie catches the puck, the last velocities space equal, or . Thus, the conservation of momentum equation simplifies toSolving because that

yieldsEntering well-known values in this equation, we get

Discussion because that (a)

This recoil velocity is small and in the very same direction as the puck’s initial velocity, together we might expect.

**Solution for (b)**

Before the collision, the interior kinetic power of the system is that of the hockey puck, because the goalie is at first at rest. Therefore, is initially

After the collision, the internal kinetic energy is

The adjust in interior kinetic power is thus

where the minus sign indicates that the energy was lost.

Discussion because that (b)

Nearly every one of the initial inner kinetic energy is lost in this perfect inelastic collision. is largely converted to heat energy and also sound.

During some collisions, the objects carry out not rod together and also less the the interior kinetic energy is removed—such together happens in most vehicle accidents. Alternatively, stored energy may be converted into interior kinetic energy during a collision. (Figure) shows a one-dimensional instance in which 2 carts on an air monitor collide, releasing potential power from a compressed spring. (Figure) encounters data from together a collision.

An air monitor is practically frictionless, so the momentum is conserved. Motion is one-dimensional. In this collision, examined in (Figure), the potential power of a compressed spring is released during the collision and is converted to internal kinetic energy.

Collisions are specifically important in sports and also the sporting and recreation industry makes use of elastic and also inelastic collisions. Let us look briefly at tennis. Recall the in a collision, it is momentum and also not pressure that is important. So, a heavier tennis racquet will have the benefit over a lighter one. This conclusion likewise holds true for various other sports—a lightweight bat (such together a soft ball bat) can not hit a hardball really far.

The ar of the affect of the tennis ball on the racquet is also important, together is the component of the stroke during which the influence occurs. A smooth movement results in the maximizing the the velocity of the sphere after affect and reduces sporting activities injuries such together tennis elbow. A tennis player tries come hit the sphere on the “sweet spot” on the racquet, where the vibration and impact are minimized and also the ball is maybe to be given much more velocity. Sporting activities science and also technologies additionally use physics concepts such as momentum and rotational motion and vibrations.

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Take-Home Experiment—Bouncing of Tennis Ball

Find a racquet (a tennis, badminton, or various other racquet will certainly do). Location the racquet on the floor and also stand ~ above the handle. Fall a tennis ball on the strings indigenous a measure up height. Measure exactly how high the round bounces. Now ask a girlfriend to host the racquet firmly by the handle and also drop a tennis ball from the same measured height over the racquet. Measure exactly how high the ball bounces and observe what happens to her friend’s hand throughout the collision. Explain your observations and measurements.The coefficient that restitution is a measure up of the elasticity the a collision in between a ball and also an object, and also is defined as the proportion of the speeds after and also before the collision. A perfectly elastic collision has actually a the 1. For a sphere bouncing turn off the floor (or a racquet on the floor), deserve to be displayed to it is in whereby is the elevation to i beg your pardon the sphere bounces and is the height from i beg your pardon the sphere is dropped. Identify for the situations in part 1 and also for the instance of a tennis ball bouncing turn off a concrete or wood floor ( for brand-new tennis balls used on a tennis court).

Calculating final Velocity and also Energy Release: 2 Carts Collide

In the collision pictured in (Figure), two carts collide inelastically. Cart 1 (denoted

dead a spring which is at first compressed. During the collision, the feather releases the potential energy and also converts that to inner kinetic energy. The fixed of dare 1 and also the spring is 0.350 kg, and the cart and the feather together have actually an early velocity of . Dare 2 (denoted in (Figure)) has a fixed of 0.500 kg and an early stage velocity of . ~ the collision, cart 1 is it was observed to recoil v a velocity of . (a) What is the last velocity of cart 2? (b) just how much power was exit by the spring (assuming all of it was converted into internal kinetic energy)?Strategy

We can use conservation of inert to find the final velocity of dare 2, due to the fact that

(the track is frictionless and also the pressure of the feather is internal). When this velocity is determined, we can compare the interior kinetic energy before and after the collision come see just how much power was released by the spring.Solution because that (a)

As before, the equation for conservation of inert in a two-object system is

The only unknown in this equation is . Resolving for and also substituting well-known values right into the previous equation yields