3 years, 1 month ago
i have a work and K.E question..please help:)
You and your bicycle have combined mass 80.0 kg. When you reach the base of a bridge, you are traveling along the road at 5.00 m/s. At the top of the bridge, you have climbed a vertical distance of 5.2 m and have slowed to 1.5 m/s. You can ignore work done by friction and any inefficiency in the bike or your legs. a) What is the total work done on you and your bicycle when you go from the base to the top of the bridge? b) How much work have you done with the force you apply to the pedals?
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M$1 Answer
To me, this question seems to lend itself to a conservation of energy approach.
At the base of the bridge, your total energy is just your initial K.E.
At the top of the bridge, your total energy is your final K.E. plus the P.E. you gain by rising height 5.2 m from the ground.
If you calculate these based on the values you give, using
KEi = KEf + PE
1/2 mvi^2 = 1/2 mvf^2 +mgh
you can easily see that they are not equal. The difference between them is the amount of work it took you to get to the top of the bridge.
I.e., the real "conservation of energy" equation (quotes added because it's not technically conservation anymore if you're adding energy to the system by means of work) should be
KEi + W = KEf + PE
For part b), isn't this just going to be the work from part a)? You're the only one doing work here--pedaling yourself to the top of the bridge.
Hope that helps!
At the base of the bridge, your total energy is just your initial K.E.
At the top of the bridge, your total energy is your final K.E. plus the P.E. you gain by rising height 5.2 m from the ground.
If you calculate these based on the values you give, using
KEi = KEf + PE
1/2 mvi^2 = 1/2 mvf^2 +mgh
you can easily see that they are not equal. The difference between them is the amount of work it took you to get to the top of the bridge.
I.e., the real "conservation of energy" equation (quotes added because it's not technically conservation anymore if you're adding energy to the system by means of work) should be
KEi + W = KEf + PE
For part b), isn't this just going to be the work from part a)? You're the only one doing work here--pedaling yourself to the top of the bridge.
Hope that helps!
source(s):
my brain
my brain
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