Question

6. Two skaters at rest, one of 120 kg and the second of 60 kg, push off against another. Which will gain the largest magnitude of momentum? A. Both skaters will gain momentum of the same magnitude B. Neither skaters will gain any momentum C. the 120-kg skater D. the 60-kg skater E. the momentum of each skater is conserved

7. Momentum changes for each of these scenarios except for A. a neutron in a nuclear reactor that changes the direction but not the magnitude of its velocity when it scatters off another neutron B. a falling rock from an instant after initial drop from a high tower until an instant before impact C. a block sliding at constant speed (with friction) down an inclined plane D. a movie stunt performer flying on a parabolic path before the performer stops on the ground E. a rocket sled on a horizontal track from an instant after the drag parachute opens until an instant before the sled comes to rest

Answer 1

Solution of 6:

We have,
Mass of skater 1
Mass of skater 2

Momentum is defined in terms of mass and velocity :

Therefore, either mass or velocity increases, the momentum of the object is increases. In this case, the initial velocity because both skaters are at rest initially.

Therefore, velocity of both skaters can be given by kinematics formula:

Where is the acceleration and is the time.

Now, according to Newton's second law acceleration can be defined as:

Where is the force and is the mass.

Now, the moment of each skater is given as:

Now, is the change of momentum or impulse.

Therefore, we can conclude that whoever the skater exerts larger force in less time will push another and gain momentum. In another word, since force can be defined in terms of mass and acceleration, therefore, whoever skater has the largest mass will push another and gain momentum.

Therefore, the correct option is C, the 120-kg skater will gain the largest magnitude of momentum.

Solution of 7:

As explained earlier, the change of momentum is the impulse.

Since neutron in a nuclear reactor that changes the direction but not the magnitude of its velocity when it scatters off another neutron, the momentum of the neutron will be constant because it only changes the direction but not magnitude, therefore, option A is not correct.

Falling rock is accelerating at gravitational acceleration which means the rock is increasing its speed at a constant rate. Therefore, when rock lands on the ground it will have high momentum due to high velocity and small momentum when it just started falling which leads to momentum change in the rock. Thus, the option B is correct.

Since a block with mass is sliding at constant speed with friction down an inclined plane, the magnitude of the momentum will be constant, therefore, option C is not correct.

The movie stunt performer flying on a parabolic path has momentum change because stunt performer is accelerating under influence of gravitational acceleration which leads to performer constantly increases their velocity. Just when performer stops at ground, they will exert high force due to high velocity in a very less time, for this reason performer will have impact and therefore, they will have momentum change. Thus, the option D is correct.

Rocket sled on a horizontal track has initial velocity but as soon as it opens the drag parachute it will have velocity change and after opening the drag parachute, the rocket is decelerating which means the velocity of the rocket is decreasing at a constant rate. Therefore, rocket will have velocity change just before coming to rest, which the velocity change leads to rocket's momentum change. Thus, the option E is correct.