Momentum and energy two sled questions for physics

[skuller]

momentum and energy two sled questions for physics...

I have tried to solve these questions but sleds to me are just very confusing and hard...I really need help with this.

A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in the figure.

a) Find an expression for the sled's speed when it is at angle theta.

b) Use Newton's laws to find the maximum speed the sled can have at angle theta without leaving the surface.

c) At what angle theta_max does the sled "fly off" the hill?


I have the picture of this problem right here...

http://img703.imageshack.us/img703/7765/sled.png









A new event has been proposed for the Winter Olympics. An athlete will sprint 100 m, starting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 50-m-long ice-covered ramp, sloped at 20 degrees , and into a spring with a carefully calibrated spring constant of 2000 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40 kg, has been training for this event. She can reach a maximum speed of 12 m/s in the 100 m dash.

here is a diagram of this i uploaded...


http://img521.imageshack.us/img521/7765/sled.png



I know for one of them I need the centripetal acceleration and for the other I need mv for momentum and spring potential energy then I am clueless

 

[Mindscrape]

Hello skuller, welcome to the forums. Don't feel bad, these are very tough questions. We generally require that you show some of your attempt before we help you out. We can't help you to gain more knowledge when we don't even know where your starting level is.

Try something out, even if you get it wrong the act of you trying will be helpful to you. If you can do the whole problem, but you get it wrong that's fine. If you do a tiny bit of the problem right, then get stuck, that's fine too.

 

[Mindscrape]

Here, I'll give you a kick-start since I see you haven't responded and must still be struggling. If you use conservation of energy you can get the velocity at any position on the semi-circle. The trick after that is to come up with the balance of forces that will tell you when the sled is about to leave the track.

 

[Mindscrape]

The second question is a bit easier and you should be able to get it through many possible methods, though once again, conservation of energy will make life easier on you.

 

[rwisz]

...

I can understand your confusion and difficulty with these questions. Momentum and energy are fundamental concepts in physics and can be quite challenging to grasp at first. Let's break down the questions and see if we can come up with some solutions.

For the first question about the sled on the hill, we can use the conservation of energy principle to find the sled's speed at any angle theta. At the top of the hill, the sled has only potential energy (mgh) and at the bottom, it has both potential and kinetic energy (1/2mv^2). We can equate these two energies and solve for the speed v.

mgh = 1/2mv^2

v = √(2gh)

Now, at any angle theta, the sled will have a component of its weight acting down the slope (mgcosθ) and a normal force pushing it up the slope (mgsinθ). The sled will only slide down the slope if these two forces are balanced, meaning the normal force equals the component of weight. So, we can use Newton's second law (F=ma) to find the maximum speed that the sled can have without leaving the surface.

mgsinθ = ma

a = gsinθ

Now, we can use this acceleration in our expression for speed to find the maximum speed at angle theta. This will give us the answer to part b of the question.

For part c, we need to consider the forces acting on the sled at the maximum angle where it will fly off the hill. At this angle, the normal force will be zero, meaning the weight of the sled will be greater than the force holding it on the slope. This force is the component of weight acting down the slope (mgcosθ). So, we can set this force equal to the maximum force of friction (μmg), where μ is the coefficient of friction. This will give us the maximum angle at which the sled will fly off the hill.

mgcosθ = μmg

θ = cos^-1(μ)

For the second question about the bobsled and spring, we can use the conservation of momentum principle to solve for the compression of the spring. At the start, the athlete and bobsled have zero momentum (since they are at rest). After the sprint, the athlete will have a momentum of mv, which will be transferred to the bobsled. The bobsled