Coasting along at 7.6m/s, a 60.0kg bicyclist on a 7.00kg bicycle encounters a small hill. If the she coasts uphill until coming to a stop, how high up the hill did she travel? (b) What height would the bike reach if she had gone to the store and had 5.50kg of groceries before coasting up the hill ?
I did Up the hill means force =2mg Sin Theta
And
Force fraction= forcegravity down the hill = mg*Sin Thera
Am I doing right ?
there is no angle of inclination specified
kinetic energy becomes gravitational potential
1/2 m v^2 = m g h
a. KE = 0.5M*V^2 = 0.5*67*7.6^2 = 1935 J.
Work = Change in KE = 1935 J. (It changes to zero).
Work = F*d = Mg*d = 1935
67*9.8*d = 1935
d = 2.95 m up hill.
b. Same procedure as part a except M = 67 + 5.5 = 72.5 kg.
It seems like you have a good start in solving the problem! Let's break it down step by step.
To determine how high the bicycle and rider travel up the hill, we need to understand the forces acting on them.
First, let's determine the force of gravity pulling them downhill. The force of gravity can be calculated by multiplying the mass (m) by the acceleration due to gravity (g), where g is approximately 9.8 m/s².
Force gravity down the hill = (mass of rider + mass of bike) * g
Next, we need to find the force component pushing the bicycle uphill. This force is equal to the force of gravity times the sine of the angle of the hill (θ).
Force uphill = Force gravity down the hill * sin(θ)
Now, we know that this force uphill is what causes the bicycle to lose speed until it comes to a stop. We can calculate how long it takes for the bicycle to stop using the equation:
Time to stop = initial speed / (Force uphill / (mass of rider + mass of bike))
Once we know how long it takes for the bicycle to stop, we can find out how far it traveled (height up the hill) using the equation:
Height up the hill = (1/2) * (Force uphill / (mass of rider + mass of bike)) * (Time to stop)²
So, to answer your first question, the height up the hill that the bicycle travels will depend on the angle of the hill (θ). You need to know the angle of the hill to calculate the force component pushing the bicycle uphill (Force uphill).
For your second question about the bike carrying groceries, the steps remain the same. You just need to add the mass of the groceries to the total mass of the rider and bicycle and then follow the same calculations as before.
Remember, to get the exact answer, you will need to know the angle of the hill (θ).