#$&*
course PHY 201
015. Impulse-Momentum*********************************************
Question: `q001. Note that this assignment contains 6 questions.
. Suppose that a net force of 10 Newtons acts on a 2 kg mass for 3 seconds. By how much will the velocity of the mass change during these three seconds?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The velocity of the mass will change by 15 m/s during those three seconds. I found this by solving for a in F=ma, then using the acceleration to solve for change in v in a=v2-v1/'dt
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Given Solution:
The acceleration of the object will be
accel = net force / mass = 10 Newtons / (2 kg) = 5 m/s^2.
In 3 seconds this implies a change of velocity
`dv = 5 m/s^2 * 3 s = 15 meters/second.
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):ok
------------------------------------------------
Self-critique rating:ok
Question: `q002. By how much did the quantity m * v change during these three seconds?
What is the product Fnet * `dt of the net force and the time interval during which it acted?
How do these two quantities compare?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The quantity of m*v changed by 225 J found by using the formula for KE. The product of Fnet * 'dt is 30 N/s. I'm not sure how these two quantities compare.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Given Solution:
Since m remained constant at 2 kg and v changed by `dv = 15 meters/second, it follows that m * v changed by 2 kg * 15 meters/second = 30 kg meters/second.
Fnet *`dt is 10 Newtons * 3 seconds = 30 Newton * seconds = 30 kg meters/second^2 * seconds = 30 kg meters/second.
The two quantities m * `dv and Fnet * `dt are identical.
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):ok
------------------------------------------------
Self-critique rating:ok
Question: `q003. The quantity m * v is called the momentum of the object.
The quantity Fnet * `dt is called the impulse of the net force.
The Impulse-Momentum Theorem states that the change in the momentum of an object during a time interval `dt must be equal to the impulse of the average net force during that time interval. Note that it is possible for an impulse to be delivered to a changing mass, so that the change in momentum is not always simply m * `dv; however in non-calculus-based physics courses the effective changing mass will not be considered.
If an average net force of 2000 N is applied to a 1200 kg vehicle for 1.5 seconds, what will be the impulse of the force?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The impulse will be equal to Fnet * 'dt or 3000. I'm not sure if I should put units next to it.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Given Solution:
The impulse of the force will be Fnet * `dt = 2000 Newtons * 1.5 seconds = 3000 Newton*seconds = 3000 kg meters/second. Note that the 1200 kg mass has nothing to do with the magnitude of the impulse.STUDENT COMMENT: That's a little confusing. Would it work to take the answer I got of 3234 N and add back in the weight of the person at 647 N to get 3881?
INSTRUCTOR RESPONSE: Not a good idea, though it works in this case.
Net force = mass * acceleration.
That's where you need to start with problems of this nature.Then write an expression for the net force, which will typically include but not be limited to the force you are looking for. *&*&
Self-critique (if necessary):ok
------------------------------------------------
Self-critique rating:ok
Question: `q004. If an average net force of 2000 N is applied to a 1200 kg vehicle for 1.5 seconds, what will be change in the velocity of the vehicle?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The change in velocity will be equal to 2.5 m/s. I found this by putting Fnet * 'dt = m * 'dv and solving for 'dv.
Confidence rating:2
Given Solution:
The impulse of the 2000 Newton force is equal to the change in the momentum of the vehicle. The impulse is impulse = Fnet * `dt = 2000 Newtons * 1.5 seconds = 3000 Newton*seconds = 3000 kg meters/second.
The change in momentum is m * `dv = 1200 kg * `dv.
Thus
1200 kg * `dv = 3000 kg m/s, so
`dv = 3000 kg m/s / (1200 kg) = 2.5 m/s.
In symbols we have Fnet * `dt = m `dv so that
`dv = Fnet * `dt / m.
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):ok
------------------------------------------------
Self-critique rating:ok
Question: `q005. Use the Impulse-Momentum Theorem to determine the average force required to change the velocity of a 1600 kg vehicle from 20 m/s to 25 m/s in 2 seconds.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Fnet = m * 'dv/'dt
Fnet = 1600 kg * (25 m/s-20 m/s / 2 seconds)
Fnet = 1600 kg * (5 m/s/ /2 seconds)
Fnet = 1600 kg * 2.50 m/s
Fnet = 4000 N
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Given Solution:
The vehicle changes velocity by 5 meters/second so the change in its momentum is m * `dv = 1600 kg * 5 meters/second = 8000 kg meters/second. This change in momentum is equal to the impulse Fnet * `dt, so
Fnet * 2 sec = 8000 kg meters/second and so
Fnet = 8000 kg meters/second / (2 seconds) = 4000 kg meters/second^2 = 4000 Newtons.
In symbols we have Fnet * `dt = m * `dv so that Fnet = m * `dv / `dt = 1600 kg * 5 m/s / ( 2 s) = 4000 kg m/s^2 = 4000 N.
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):ok
------------------------------------------------
Self-critique rating:ok
If you understand the assignment and were able to solve the previously given problems from your worksheets, you should be able to complete most of the following problems quickly and easily. If you experience difficulty with some of these problems, you will be given notes and we will work to resolve difficulties.
*********************************************
Question: `q006. ‘Each time they thought they had ‘im, his engine would explode. He’d go by like they was standin’ still on Thunder Road.’ Good song. If you don’t know it you might want to look it up and listen to it (the name is 'Thunder Road').
His car, including him and his load, had a mass of 2500 kg. To escape, he had to speed up from 35 m/s to 45 m/s. How much impulse did he need from his engine?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Initial KE =15.3x10^5 J
Final KE= 25.3 x10^5J
Work Done= 10 x 10^5 J
@&
This is correct, but it doesn't answer the question.
Impulse is equal to change in momentum, not change in kinetic energy.
*@
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&#This looks good. See my notes. Let me know if you have any questions. &#