I was wanting help with my physics post and since no one replied I thought there wasn't a physics tutor on Jiskha, but came back on today cause I really need to get a hang of my physics stuff and luckily seen you Drwls.
A bike rider approachea a hill with a speed of 8.5m/s. The total mass of the bike and rider is 85kg.
A. Find the kinetic energy of the bike and rider.
Formula for Kinetic Energy I got given is...
Ek = 1/2mv62
1/2(85)(8.5)^2
= 3070.6J
^ That was the easy part. But ughh I am hating the second part to it so much.
The rider coasts up the hill. Assuming there is no friction, at what height will the bike come to a stop?
I have no idea what formula to use to solve the question. Formulas I'm given are...
Egp = mgh
Ek = 1/2mv^2
Eh = mcT
Ee = 1/2kx^2
All these formulas are driving me crazy. My teacher with one question did this.. ET = ET'
Ek + Egp = Ek' = Egp
1/2mv^2 + mhg = 1/2mv^2 + mgh
And the mass crosses out for some odd reason. But before we get to this, I seriously need to know meaning of those formulas. Physics is not my strong area, just took this subject because I may need it in the future. But please help.
And the third part to that.
Does your answer depend on the mass of the bike and rider? Explain.
I guess not because there is no friction, but still how would that take away mass? I mean if I were on frictionless ice standing on top of it, my mass wouldn't automatically be erased :\
The answer will not depend upon the mass of the bike and rider. That will cancel out.
Coasting up the hill, the bike will stop when the initial kinetic energy equals the potential energy increase, M g H. H is the increase in altitude.
Vo^2/2 = g H
Solve for H.
Strictly speaking, the initial kinetic energy is higher because of the rotating wheels, but that additional effect is negligible since the wheels are usually a small fraction of the total weight.
I understand that you're looking for help with your physics problem. Let's break down the problem step by step and explain the formulas along the way.
First, you correctly found the kinetic energy of the bike and rider as 3070.6J using the formula:
Ek = 1/2mv^2
Now, onto the second part of the question: "The rider coasts up the hill. Assuming there is no friction, at what height will the bike come to a stop?"
To solve this, we will use the principle of conservation of mechanical energy. This principle states that the total mechanical energy of a system remains constant if no external forces, like friction, are acting on it.
The total mechanical energy of a system consists of two components: kinetic energy (Ek) and gravitational potential energy (Egp).
Now, let's look at the formula you mentioned: ET = ET'
ET represents the total mechanical energy at the start, and ET' represents the total mechanical energy at the end.
Ek + Egp = Ek' + Egp'
On the left side, we have the initial kinetic energy (Ek) and initial gravitational potential energy (Egp). On the right side, we have the final kinetic energy (Ek') and final gravitational potential energy (Egp').
Since the rider comes to a stop at the top of the hill, the final kinetic energy (Ek') is zero.
0 + Egp = 0 + Egp'
Now we can simplify it:
Egp = Egp'
The gravitational potential energy of an object near the surface of the Earth is given by the formula:
Egp = mgh
Where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
So now we have:
mgh = mgh'
Since the mass (m) is common on both sides, it cancels out:
gh = gh'
Finally, we can solve for the height (h'):
h' = h
This means that the final height (h') at which the bike comes to a stop is the same as the initial height (h) from which the rider started coasting up the hill. Therefore, the answer does not depend on the mass of the bike and rider.
Regarding your question about the mass: In this specific scenario where there is no friction, the mass of the bike and rider does not affect the final height. This is because gravitational potential energy depends on mass and height, but when the mass cancels out in the equation, it means that the mass does not play a role in determining the final height.
I hope this explanation helps you understand the problem better. If you have any further questions, feel free to ask!