Physics: Momentum and Collisions help?

Question

I need help on some of these problems. It would be great if you could include how you got the answer too.
1. If object A has twice the mass of object B and has twice the speed of B, then how do their momentums compare?

2. Bill drives his car at 20 m/s and applies the brakes to stop in 4s. Later he stops his car from the same speed in 2s. How do the impulses applied by the brakes compare?

3. Bill drives his car at 20 m/s and applies the breaks to stop in 4s. Later he stops his car from twice the original speed in the same time. How do the impulses applied by the breaks compare?

4. A rifle has a mass of 5kg and fires a 10g bullet at 300m/s. What is the recoil speed of the rifle?

5. Car A (m=1000kg) is going East at 5m/s. Car B (m=2000kg) is going South at 5m/s. What is the the resulting velocity of the cars if they undergo an inelastic collision?

6. What is the difference between linear force and torque?

Answer 1

1.) ok, I'm assuming "A" if double fat and double fast



Let x=mass of "B"

& Let y=velocity of "B"



so

mass of "A" = 2x

& velocity of "A" = 2y



ok so you know that the "cool momentum equation" is Moe= Fat * Fast or P=m*v



for "B" (Pb = the Momentum for "B")

=Pb

= x * y

= 1 * x * y

= 1xy



for "A" (Pa = Momentum for "A")

= Pa

= 2x * 2y

= 2 * x * 2 * y

= 2 * 2 * x * y

= 4 * x * y

=4xy





So you can see that object "A" is four times as awesome as object "B" with respect to momentum



2.) V= 20m/s (ta=Time for the first event) ta=4s (tb=Time for the second event) tb= 2s



You need to understand that 'breaking' in a car is accelerating but negatively, so lets use the "cool acceleration equation" a = v / t



For event one: (aa = acceleration for the first event)

= aa

= 20m/s / 4s

= 5m/s^2



For event two: (ab = acceleration for the second event)

= ab

= 20m/s / 2s

= 10m/s^2



you can see in that the second event caused some serious break mashing on Bill's part, he stopped with twice the acceleration negatively.



3.) Va = 20m/s Vb = 40m/s t = 4s



For event one:

= aa

= 20m/s / 4s

= 5m/s^2



For event two:

= ab

= 40m/s / 4s

= 10m/s^2



(ctrl-C, ctrl-V) you can see in that the second event caused some serious break mashing on Bill's part, he stopped with twice the acceleration negatively.



4.) mass of rifle = 5kg mass of bullet = 0.01kg velocity of bullet = 300m/s



Now remember what Sir Newton always says about his number one: "every action has an equal and opposite reaction"

this applies to force quite awesomely. Oh, and use that rapscallion's number two "cool force equation" F=ma





The Force of the bullet:

= F of bullet

= 0.01kg * 300m/s^2

= 3N



ok so number one says that, the force the gun gives the bullet to gtho will be the same force the bullet gives the gun as it dipsets outa there.



The Force of the recoil = The Force of the bullet

The Force of the recoil = 3N



I'll just transform the "cool force equation" into "cool acceleration equation w/ force" ("qooqeequrrkoo") a=F/m ("ROLL OUT!")



The Acceleration of the recoil:

= a of recoil

= 3N / 5kg

= 0.6m/s^2



NOTE: this question was odd, it had stated that the bullet left at a velocity of 300m/s however it did not say at what time it reached 300m/s, so to make things easy for me I was all like "well lets just say something like 1second so I can use the acceleration and velocity interchangeably" but keep in mind I also assumed that the time at which the speed of the recoil was being measured was the same time that the speed of the bullet was being measured. That means I could have made it any amount of time, and the answer would still be the same.



So the recoil speed of the rifle is 0.6m/s



5.) This is really cool to do with a drawing but wtc let me try it w/o



remember that "cool momentum equation"? P=mv



Car A's Fat = 1000kg Car A's Fast = 5m/s [E]

Car B's Fat = 2000kg Car B's Fast = 5m/s [S]



Car A's Momentum:

= Pa

= 1000kg * 5m/s [E]

= 5000kgm/s [E]



Car B's Momentum:

= Pb

= 2000kg * 5m/s [S]

=10000kgm/s [S]



this is the part where a drawing would be useful



The angle from south = theta



theta = (1/tan) (car A's momentum / car B's Momentum)

= (1/tan) (5000kgm/s / 10000kgm/s)

= (1/tan) (1/2 kgm/s)

= 26.565051177077989351572193720453°

or = 27°



= the added momentum

= ((5000kgm/s)^2 + (10000kgm/s)^2)^(1/2)

= 11180.339887498948482045868343656kgm/s

or = 11000kgm/s



= the added mass

= 1000kg + 2000kg

= 3000kg



now we need to find the velocity from the momentum using "cool velocity equation w/ momentum"

v = P/m



= the resulting speed

= P/m

= 11180.339887498948482045868343656kgm/s / 3000kg

= 3.7267799624996494940152894478855m/s

or = 3.7m/s



so the resulting velocity is 3.7m/s [S 27° E]



6.) liner force is a force that acts upon an object in a single direction

torsional force is force applied on something that twists

it is caused by a linear force sort of. To calculate the torsional force applied to something like the second hand on a clock being pushed by a finger, use this cool equation



T = F * r * sin theta

where:

T = torque

F = The linear force applied by the finger

r = the distance from the fulcrum on the second hand where the force is being applied

theta= the angle between the second hand and the linear force applied by the finger (it's usually 90° so it ends up being 1 and not making a difference)

Answer 2

If both cars are traveling opposite directions and they collide head on? conservation of linear momentum. if the velocities are the same, then the cars will travel in the direction of the larger car after the collision, but at a slower speed. The collision will be inelastic. Weather or not it is completely inelastic depends. At a higher speed the cars will likely mesh together in the crumple metal and result in a perfectly inelastic collision.

Answer 3

1. Momentum = mass x velocity, so the momentum of A equals twice the mass of B times twice the velocity of B, which is four times the momentum of B.



2. 20/4=5 m/s^-1, and 20/2= 10 m/s^-1



3.40/4 = 10 m/s-1, so it is double the previous result



4. 0.001kg x 300 m/s = 0.3 kg m/s

0.3 kg m/s / 5 = 0.06 m/s



5. 15,000 kg m/s / 3,000 kg = 5 m/s South-east



6. Linear force happens in a straight line (linear), while torque usually happens in a circular motion.