Answer:
A) The smaller object; B) The larger object
Explanation:
A) Lets say the small object is 2 kg and the large one is 6 kg. Lets say they also have 30 kg*m/s of momentum each. The small object would have 15 m/s velocity and the large would have 5 m/s.
Now for kinetic energy(.5*m*v²), the small object is .5*2*15², which is 225 J
The large object is .5*6*5², which is 75 J, so the smaller object has more Kinetic energy. Since velocity is squared, it is more important than how large mass is.
B) Same masses as part A. Lets say the kinetic energy is 45 J for both of them. For the small object, 45=.5*2*v²
.5*2 is 1, so 45/1 is 45. Take the square root and we get v= 6.71 m/s
For the large object, 45=.5*6*v²
.5*6 is 3, so 45/3 is 15. Take the square root and we get v=3.87 m/s
Now we plug the velocities into p=mv
For the small object, p=2*6.71, which gives us p=13.42 kg*m/s
For the large object, p=6*3.87, which gives us p=23.22 kg*m/s
The larger object has the larger momentum.
Hope this helps
Using the relationship between and velocity, mass, momentum and kinetic energy through mathematical illustration ;
Recall :
To test the conditions above :
Find the velocity of the objects :
Small mass :
20 = 2v
v = (20/2) = 10 m/s
Large Mass :
20 = 4v
v = (20/4) = 5 m/s
B.)
Small mass :
100 = 0.5mv²
100 = 0.5×2×v²
100 = v²
v = √100
v = 10 m/s
Momentum = 2 × 10 = 20 kgm/s
Large mass :
100 = 0.5mv²
100 = 0.5×4×v²
100 = 2v²
50 = v²
v = √50
v = 7.07 m/s
Momentum = 4 × 7.07 = 28.28kgm/s
Therefore, smaller object has greater kinetic energy while larger object has a larger momentum.
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