How Can Conservation of Energy Determine Projectile Height and Bead Speed?

[Spitting_Camel]

Supposed Energy Problems..Help!

I have 2 questions...

A projectile is launched with a speed of 40 m/s at at angle of 60 degrees about the horizontal. Find the maximum height reached by the projectile during its flight by using conservation of energy.

I guess I don't get how to get the answer from a bunch of work, PE and KE equations. If you could give me a hint on this one on where to start, what equations to use I can probably figure it out.
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Second question...

A bead of mass m=5.00kg is released from point A and slides on the frictionless track shown in figure P5.30. Determine (a) the bead's speed at points B and C and (b) the net work done by the force of gravity in moving the bead from A to C.

I am also completely lost on this question too. I don't understand how you can get speed (v) from any of the work, PE, KE equations. Please give me a hint! I attached a crude picture of the graphic for this one...

Thank you so much if you respond.

 

[stunner5000pt]

first question

dK + dU = 0

KE ( final) - KE ( initial) + PE ( final) - PE (initial) = 0

what is the velocity of the ball when it reaches th highest point? Who cares about angles, talk about vertical speed, if the ball were throw staright up, woul it make a difference? I know you've been shown this in class

What is the initial velocity? Find the VERTICAL velocity of the ball using the angle that you are given

What is the initial height? Was it shot from the ground or from a height? in that case what is vakue of initial height?

What is final height? given all these clues can you figure it out?

 

[wais]

First, let's address the projectile problem. To find the maximum height, we need to use the conservation of energy principle, which states that the total energy of a system remains constant. In this case, the initial energy (at the launch point) will equal the final energy (at the maximum height). We can use the equations for potential energy (PE) and kinetic energy (KE) to solve for the maximum height. Here's a hint: at the maximum height, the projectile's velocity will be zero, so the kinetic energy will also be zero. This means that all of the initial energy will be in the form of potential energy at the maximum height. Can you take it from there?

For the second question, we can use the same principle of conservation of energy. At point A, the bead has potential energy due to its height above the ground. As it travels down the track, this potential energy is converted into kinetic energy. At point C, all of the potential energy has been converted into kinetic energy, so we can use the equation for kinetic energy to find the speed at point C. To find the speed at point B, we can use the conservation of energy principle again, this time using the kinetic energy at point B as the initial energy and solving for the final kinetic energy at point C. As for the net work done by gravity, we can use the equation W = Fd, where F is the force of gravity and d is the distance traveled. Can you try using these hints to solve the problem? Let me know if you need further clarification. Good luck!