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Mechanics force, mass and momentum of an object

Q. An object sitting on a smooth surface is given an impulse (force) to start from rest and reached a veloctiy of 5m/sec in 2 seconds.

1. What is the mass of the object if the applied force was 20 N

2. What is the change in momentum

3. At the time given above the object is travelling towards the northwest with an angle of 45 degrees with the horizontal and hit another object mass of 5 kg, which was travelling at 10m/sec toward the east and combined together. what is the final velocity and which direction? hint use the law of conservation of momentum and treat the momentum as vectors.

Solution Preview

To solve this problem, I will use the following formulae on motion :
(I assume that you have seen and used these before)
(i) v=u+at
(ii) s=ut+0.5*a*t^2
(iii) v^2=u^2+2as

where u=initial velocity;v=final velocity; a=acceleration; s=distance; t=time.

Also, from Newton's Law we get:
(iv)Force(F) = Mass(m)*accelern.(a) = m*(v-u)/t
(v) Thus, F*t = m*(v-u) = change in momentum.

1. In the first part, it is given that the object starts from rest, (thus 'u=0') and reaches a velocity 'v=5 m/sec' in time 't=2 secs'.
Putting these values in eqn.(i), we get the acceleration a=2.5 m/sec^2. Using eqn. (iv), F=m*a, and given that F= 20N, we get the mass(m)= F/a = 20/2.5= 8 kg.

2. To calculate change in momentum, note that Momentum(p) is defined as Mass*Velocity. So in our case the Mass is constant at 8kg and the velocity changes from u=0 to v=5m/sec. So the change in momentum is(from ...

Solution Summary

The solutions are clear and carefully explained with all the calculations.