Calculate the change in momentum in each of the following situations and state the direction of the change in momentum.
a) A 4kg bowling ball strikes a stationary pin head-on at a speed of 3m/s. It continues to move in its original direction, but its speed is reduced to 2m/s.
b) A 200g rubber ball falling vertically strikes ground at a speed of 10m/s and bounces vertically upwards, leaving ground at speed of 6m/s.
c) A 4kg bowling ball moving at 2.5m/s strikes a pin in a glancing fashion. It is deflected through an angle of 10degrees. It's speed is reduced to 2m/s.
Can someone please explain how change in momentum can be calculated first of all and then go over the those questions and please explain what you did.
Sorry for the triple-post. Please ignore whichever immature person answers this using my name.
momentum can be found by multiplying mass and velocity together.
a) (4kg)(3m/s)-(4kg)(2m/s)
Use the definition of change in momentum, a vector operation.
changeinmomentum= Finalmomentum -initial momentum
= massfinal(velocityfinal)-massinitial(velocityinitial)
= mass (Vf-Vi)
Now remember, you have direction associated with Vf and Vi.
To calculate the change in momentum, you can use the equation:
Change in momentum = Final momentum - Initial momentum
The momentum of an object with mass "m" and velocity "v" is given by the equation:
Momentum = mass * velocity
Now, let's go through each situation and calculate the change in momentum:
a) In this situation, we have a 4kg bowling ball moving at a speed of 3m/s. It strikes a stationary pin head-on and continues to move in its original direction, but its speed is reduced to 2m/s.
To calculate the change in momentum, we first need to find the initial momentum and the final momentum of the ball.
Initial momentum = mass * initial velocity
Final momentum = mass * final velocity
Initial momentum = 4kg * 3m/s = 12 kg m/s
Final momentum = 4kg * 2m/s = 8 kg m/s
Change in momentum = Final momentum - Initial momentum
Change in momentum = 8 kg m/s - 12 kg m/s = -4 kg m/s
The negative sign indicates a change in momentum in the opposite direction of the initial momentum. In this case, the change in momentum is -4 kg m/s, indicating that the momentum decreased.
b) Here, we have a 200g (0.2kg) rubber ball falling vertically and striking the ground at a speed of 10m/s. It bounces vertically upwards and leaves the ground at a speed of 6m/s.
Similarly, we calculate the initial and final momentum to find the change in momentum.
Initial momentum = mass * initial velocity
Final momentum = mass * final velocity
Initial momentum = 0.2kg * 10m/s = 2 kg m/s
Final momentum = 0.2kg * (-6m/s) = -1.2 kg m/s
Change in momentum = Final momentum - Initial momentum
Change in momentum = -1.2 kg m/s - 2 kg m/s = -3.2 kg m/s
Again, the negative sign indicates a change in momentum in the opposite direction of the initial momentum. In this case, the change in momentum is -3.2 kg m/s, indicating a decrease in momentum.
c) In this scenario, a 4kg bowling ball moving at 2.5m/s strikes a pin in a glancing fashion. It is deflected through an angle of 10 degrees, and its speed is reduced to 2m/s.
To calculate the change in momentum, we once again find the initial and final momentum.
Initial momentum = mass * initial velocity
Final momentum = mass * final velocity
Initial momentum = 4kg * 2.5m/s = 10 kg m/s
Final momentum = 4kg * 2m/s = 8 kg m/s
Change in momentum = Final momentum - Initial momentum
Change in momentum = 8 kg m/s - 10 kg m/s = -2 kg m/s
As before, the negative sign indicates a change in momentum in the opposite direction of the initial momentum. In this case, the change in momentum is -2 kg m/s, indicating a decrease in momentum.
It is important to note that the direction mentioned (head-on or glancing fashion) is used to describe how the objects collide or interact, but it does not affect the calculation of the change in momentum.