Physics Momentum and Impulse

Physics
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A 74.8kg mountain bike rider takes a jump with his bike and lands with a downward velocity of 4.43m/s 

a) what is the average net upward force the springs on the bike frame must exert to stop the downward motion in 0.416s?

b) what is the TOTAL average upward force the springs on the bike frame must exert to stop the downward motion in 0.439? 

Answer:

a) 797N     b) 1490N

I understand question a but when I try question b I cannot get the right answer. Please help.

Apr 23rd, 2015

According to the 2nd Law of Motion, the average net force is F = ma, where m = 74.8 kg and a is the average acceleration. The latter can be found as v / t (the change of velocity divided by the time, the final speed is 0).

So, in a)  F = mv/t = 74.8 kg * 4.43 m/s / 0.416 s = 797 N ( note that the force can be also found from the equation m*(v - 0) = F*t, that is the change in momentum equals impulse).

In b) we need to find the total force. There are two forces acting on the bike when it lands: its weight W = mg and the reaction force N which is equal to the upward force exerted by the springs. The net force, F = N - W, and its impulse is F*t = m*(v - 0). Then N = W + F = mg + mv/t = 74.8 * 9.81 + 74.8 * 4.43/0.439 = 

733.8 + 754.8 = 1488.6 = 1490 N (rounded to 3 significant figures).  

Apr 23rd, 2015

Thank you! I just need to ask how you knew the difference between the two questions. When I read it I thought they were both asking the same thing only using different times. Never would I have though to add Net Force and Weight. Why didn't question a need weight to be accounted for? How do I know for next time if the question is asking me to add two forces? 

Apr 23rd, 2015

I just looked at the statement of the problem and noticed that in question a) they required to find the net force and in the question b) the TOTAL force. Usually the net force is the resultant of several forces acting on a body. The weight is one of them and there should be another force opposite to the weight and even larger than it in order to stop the falling bike. 

Apr 23rd, 2015

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Apr 23rd, 2015
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Apr 23rd, 2015
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