Team Quanta gladly presents all possible short questions of BS Physics book Mechanics – I’s Chapter#04: System of Particles for the ease of students.
Define impulse and how it is related with linear momentum.
[latexpage]
Answer: Impulse is defined as product of force and time interval i.e. I= F × t provided time interval is small for which force acts.
$I=ma\times t=\ \ m\ \left(\frac{v-v_0}{t}\right)\times t$
By first equation of motion $\rightarrow I=mv-mv_0=$ Change in linear momentum
Two objects have equal kinetic energies. How do the magnitudes of their momenta compare?
Answer: Two objects of same mass travelling at the same speed have the same kinetic energies and the same momentum. It is also possible for a particular combination of masses and velocities and to satisfy K1=K2 but not p1=p2
Does the center of mass of a solid object necessarily lie within the object? If not, give example.
Answer: The center of object may not lie with in the object. For example there is no dough at center of mass of a doughnut and no iron at center of mass of horseshoe.
A ball is released and fall toward the ground with no air resistance. Which is the isolated system for which momentum is conserved; the ball or the ball and the earth?
Answer: Since ball and the earth exert forces on each other so isolated system must include both ball and earth to conserve linear momentum.
A man firing a loaded guns advised to press the gun against his shoulder. Why?
[latexpage]
Answer: Consider a gun of mass M loaded with a bullet of mass m. Let v be muzzle velocity of bullet and V be velocity of recoil of gun, then by law of conservation of linear momentum ,
$MV+mv=0\ \rightarrow V=-\left(\frac{m}{M}\right)\ v$
Negative sign shows recoil of gun. However V<<v as m <<M. This explains why man firing a loaded gun is, advised to press the gun against his shoulder.
Explain why under certain conditions, the law of conservation of linear momentum is useful even though the system is not completed isolated.
Answer: The system in which external forces are very small as compared to mutually interacting forces are not completely isolated. The law of conservation of momentum is useful to be applied to motion of rockets and firing of gun, ignoring frictional forces and we get approximately accurate results.
A car and a large struck travelling at the same speed makes ahead-on collision and stick together. Which vehicle experiences the larger change in the magnitude of momentum?
Answer: Both vehicle experiences same change in linear momentum since for p1 + p2 = constant, then However, change in velocity of car is greater.
Why do we use soft packing material in between the glass wares?
Answer: Due to mishandling, glass wares collide with each other and soft packing material is compressed. It provides greater time for their change of momentum and resulting in a less force acting on glass wares.
A table-tennis ball is thrown at a stationary bowling ball. The table-tennis ball makes a one-dimensional elastic collision and bounces back along the same line. After the collision, compared to the bowling ball, the table tennis ball has a smaller magnitude of momentum and more kinetic energy. Explain.
[latexpage]
Answer: By law of conservation of momentum, momentum of the two-ball system is conserved. Since the table tennis ball bounces back from the massive bowling ball with approximately the same speed, so from the relation $k= \frac{p^2}{2m,}$ the larger masses of the bowling ball has its kinetic energy smaller than that of the table-tennis ball.
Why aero plane cannot fly in space while a rocket can do so?
Answer: The aero plane uses oxygen for combustion of fuel. In space there is no oxygen, so aero plane cannot fly in space. In rocket fuel and liquid oxygen are present to burn out. The hot gasses rush out from tail of rocket and by 3rd law of motion rocket moves ahead.
Why does a cricket player retraces his hand backward while catching?
[latexpage]
Answer: A cricket player does so because it will allow him to have greater time for change in momentum. From relation,
$F=\ \frac{dp}{dt}$
When dt is large, ball will exert a less force on hand of player.
A rocket is moving upward with acceleration 3g. Calculate effective weight of an astronaut sitting in rocket when his actual weight is 75 kg.
Answer: Let M be mass of man. Forces acting on man are:
$R-MG=Ma$
Weight Mg acting vertically downward and reaction are R of floor in upward in direction. If rocket is moving up with acceleration a, then Apparent weight = R= M(g + a) = 75kg(g+3g) = 300g
When a ball of mass 10kg moving with 20m/s velocity collides elastically with an identical ball at rest in one dimension, what is the velocity of 1st ball after the collision?
Answer: The 1st ball comes to rest after collision and 2nd ball moves with velocity of 20m/s.
A ball of clay is thrown against a brick wall. The clay stops and sticks to the wall. Is the law of conservation of linear momentum violated in this process?
Answer: Law of conservation of momentum is not violated because the system is not only clay; instead system is earth along with the clay. When the clay receives an impulse backwards, the earth receives the same size impulse forwards. The resulting acceleration of the Earth due to this impulse is smaller than the acceleration of the clay, but the earth absorbs all of the momentum that the clay losses.
A glass striking on concrete is likely to break into pieces as compared to striking with cotton.
Answer: Concrete is very hard as compared to cotton , due to which collision time of glass with concrete is small as compared with cotton and force will be large .Hence glass will break on collision with concrete.
Can the center of mass of an object be located at a position at which there is no mass? If so, give examples.
Answer: Yes, center of mass of an object may be located at a position at which there is no mass. For example, a boomerang, a stool.
If a ball negligible mass moving with velocity 30m/s collide with a massive stationary target elastically in one dimension, what will be the final velocities?
Answer: Massive target remains at rest small ball reverses its direction with same velocity after collision.
A sharpshooter fires a rifle while standing with the butt of the gun against her shoulder. If the forward momentum of a bullet is the same as the backward momentum of the gun, why is not it as dangerous to be hit by the gun as by the bullet?
Answer: Since the speed of the rifle is less than the bullet so it has less kinetic energy. Moreover the rifle distributes the recoil force over an area much larger than that of the bullet; hence it is not dangerous to be hit by the gun as by the bullet.
lifting one foot into air , one balance on the other foot. Where does center of mass lie?
Answer: Center of mass lies directly above the surface of contact between foot and ground.
If two particles have equal kinetic energies, are their momenta necessarily equal?
Answer: No, the momentum of two particles will only be the same if the particles are of the same mass.
The moon revolves around the Earth. Model its orbit as circular. Is the linear momentum of moon conserved? Is its kinetic energy conserved?
Answer: No, linear momentum is not conserved since an external force of gravity acts on the moon. Yes, the kinetic energy is conserved because its speed is constant.
Point out the applications of collision phenomena.
Answer: Collision is used in thermalization of neutrons emitted from a disintegrating nucleus for many practical purposes; slowing down of neutrons by introducing matter in their path as target is called thermalization of neutrons. Normally protons and hydrogenous materials as used as target. Collision is also used in gasses exerting pressure, fission and fusion reactions and high energy physics.
If you are standing on ground and then you take a step forward . Before the step, momentum is zero, but afterward you have some momentum. Is this a violation of law of conservation of momentum?
Answer: No, the law of conservation momentum is not violated .Both before and after step momentum is zero. The reason is that earth is too massive as compared to foot that its velocity is too small to be detected.
Does a larger net force exerted on an object always produce a larger change in the momentum of the object compared with a smaller net force?
Answer: Since the impulse depends on the force and the time interval during which it is applied, so a larger force exerted on an object cannot produce a larger change in the momentum of the object compared with a smaller net force.
Differentiate between collision and scattering.
Answer: When two or more bodies come close to each other so that there is interaction between them, we say that collision has taken place. The collision is called scattering if nature of bodies does not change after collision.
If you jump from a table and land with your knees locked, why are you more likely to be hurt than if you land with your legs relaxed?
Answer: If one lands with knees locked and does not bend knees, collision time with ground will be short and as a result force will be large according to and you might be hurt. On the other if one lands with relaxed legs and bends legs, collision time will be greater and force will be lower and no danger to hurt.
Suppose you are buying apples from bazaar, if some apples drop on ground, their momentum increases. Is this violation of law of conservation of momentum?
Answer: The momentum of apples increases as they fall. The momentum of the universe remains same because an equal and opposite forces act on ground.
Explain why a head-on collision is likely to be more dangerous than other types of collisions.
Answer: In a head-on collision , a large portion of the incident kinetic energy is transformed to the other forms of energy as compared to other types of collision. Thus, head-on collision is more dangerous.
When a bullet is fired from the gun, both have equal and opposite momentum. Whether both have same kinetic energy?
Answer: Linear momentum and kinetic energy are related by,
$k=\frac{p^2}{2m}$
Above equation shows that object having small mass has greater kinetic energy although momenta are equal. Therefore bullet has greater kinetic energy.
If a system of particles has zero kinetic energy, whether its momentum is zero or not? Explain.
Answer: Linear momentum and kinetic energy are related by,
$k=\frac{p^2}{2m\ }\ \ \ \ \ \ \rightarrow p=\sqrt{2mk}$
This equation shows that if kinetic energy is zero, linear momentum is also zero.
A car of mass M collides and sticks to another identical car being at rest. What happens to the kinetic energy after collision? Relate it with kinetic energy before collision.
Answer: After collision mass is doubled and speed is halved. Hence final kinetic energy is half of initial kinetic energy.
If two automobiles collide, they usually do not stick together. Does this mean the collision is elastic?
Answer: No, for collision to be elastic, law of conservation of kinetic energy must hold. As such in this , there is loss of kinetic energy during collision.
An airbag in an automobile inflates when a collision occurs, which protects the passenger from serious injury. Why does the air bag soften the blow?
Answer: We know that,
$F=\frac{dp}{dt}=\ \frac{J}{dt}$
In the collision, the passenger must undergo a certain change in momentum. This means that a certain impulse must be exerted on the passenger. By increasing the distance over which the momentum change occurs, the time interval during which this change occurs is also increased and hence the force on the passenger is decreased.
A juggler juggles three balls in a continuous cycle. Any one ball is in contact with one of his hands for one fifth of the time. Describe the motion of the center of mass of the three balls.
Answer: The center of mass moves around in a little closed loop like parabola with a circular bottom, making three revolutions for every one revolution that one ball makes.
A massive tractor is rolling down a country road. In a perfectly inelastic collision, a small sports car run into the machine from behind. Which vehicle experiences a change in momentum of large magnitude?
Answer: In a perfectly inelastic collision, momentum of system is conserved. Hence whatever momentum one vehicle losses the other vehicle gains
Does the center of mass of a rocket in free space accelerate? Can the speed of a rocket exceed the exhaust speed of the fuel?
Answer: In empty space, during a burn, the center of mass of a rocket system does not accelerate, because no outside force acts on this system. However the rocket ( without fuel mass ) accelerates as a reaction of exhaust gasses.
The speed of a rocket can exceed the exhaust speed of the fuel if the final mass is less than 37% of the original mass.
A car of mass m travelling at speed v crashes into the rear of a truck mass 2m that is at rest and in neutral at an intersection. If the collision is perfectly inelastic , what is the speed of the combined car and truck after the collision?
Answer: By law of conservation of momentum, we have
$mv+2m\left(0\right)=\left(m+2m\right)\ V\ =mv=3mv=\ \rightarrow V=\frac{v}{3}$
While in motion, a pitched baseball carries kinetic energy and momentum. Can the baseball deliver to the bat and batter more momentum than the ball carries initially? If yes, explain. If not, give an example.
Answer: A baseball can deliver more momentum in collision than it possess in its flight, by bouncing from the object it strikes.
An open box slides across a frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower falls vertically downward into the box?
Answer: As there are no external horizontal forces acting on the box, so its momentum cannot change as it moves along the horizontal surface. As the box slowly fills with water, its mass increases with time and hence its speed decreases.
The kinetic energy of an object is increased by a factor of 4. By what factor is the magnitude of its momentum changed?
Answer: Kinetic energy and linear momentum are related by equation,
$K=\frac{1}{2}mv^2=\frac{m^2v^2}{2m}=\frac{p^2}{2m}$
This equation shows that when the speed of the rocket becomes 2 times larger, then linear momentum becomes two times larger.
A bomb, initially at rest, explodes into several pieces. Are the linear momentum and kinetic energy of the system(the bomb before the explosion , the pieces after the explosion) conserved?
Answer: Linear momentum is conserved in both types of collision. Kinetic energy is not conserved because some energy is converted to kinetic energy of the pieces of the bomb.
A massive tractor is rolling down a country road. In a perfectly inelastic collision, a small sports car run into the machine from behind. Which vehicle experiences a change in kinetic energy?
Answer: Kinetic energy and linear momentum are related by equation,
$K=\frac{1}{2}\ mv^2=\ \frac{m^2v^2}{2m}=\frac{p^2}{2m\ }$
This equation shows that the fast moving car losses more energy than the slow moving tractor gains because a lot of the car’s original kinetic energy is converted into internal energy.
Does a larger net force always produce a larger change in kinetic energy than a smaller net force?
Answer: Since the work done depends on the force and on the displacement over which it acts, so a large force cannot produce a larger change in kinetic energy than a smaller net force.
Two students hold a large bed sheet vertically between them. A sweeper throws an egg at the center of the sheet. Explain why the egg does not break when it hits the sheet, regardless of its initial speed.
Answer: The sheet increases the time interval so that the stopping force is not so large that can break egg.
