physics: Work and Energy?

Question

1. A roller coaster car rolls over the crest of a 30m high hill at a speed of 3.2m/s. The car then rolls down the track to the bottom of the hill and continues up the next hill, which is 20m high. Determine the speed of the car at the top of the second hill.

2. Maria wants to dive from the seaside cliff, but she does not feel safe hitting the water faster than 20m/s (44mi/h). What is the maximum height from which she dive?

Answer 1

Basically, you need to apply the principle of energy conservation. In both of these problems total mechanical energy is conserved. This means that the sum of potential and kinetic energy is always constant.

PE + KE = ME

We have gravitational potential energy in both cases and translational kinetic energy in both cases. This means that

ME = m g h + 1/2 m v^2

Since only height and velocity vary, you can rewrite this as:

ME0 = MEf = constant

m g h0 + 1/2 m v0^2 = m g hf + 1/2 m vf^2,

where h0 is initial height, v0 is initial velocity, hf is final height and vf is final velocity.

Basically you plug it the known values and solve for the unknown that you want to find.

NOTE: You do not need to know mass at any point in time as it is in every term of the conservation equation. The equation may be written as:

g h0 + 1/2 v0^2 = g hf + 1/2 vf^2

Answer 2

They arn't work and energy questions. They are kinematics.

But the 2nd one is much easier.
Because you know the Initial Velocity, Final Velocity (Vi, Vf), and acceleration, you will use the equation
Y (distance) = ((Vf)^2-(Vi)^2)/2a
(a = g, -9.80 m/s^2)
Vf = 20 m/s
Vi = 0 m/s
(20^2)/(2*-9.8)
You get: -20.41 m
the negative just indicated you are going down, ignore it.
20.41 meters high is the answer.
*This is how I would do that problem, no gurantee's that it is right.


As for your first problem, i recommend drawing a diagram to visualize what happens, you will need to take gravity into consideration in terms of X and Y directions (resolve with cos and sin), you will need to know the angles, if you dont have them, then there is a way to A. Solve for tha angles, or B. they are not needed (which is most likely the case).

Answer 3

once you dropped the water drop into the pool, it switched over ability power into kinetic power because it fell down. It hit the floor of the pool and did here: a million. Make a noise 2. furnish a definite volume of power to the pool of water which a. raised the temperature of the pool ever so somewhat b. led to a ripple to ensue and unfold out c. pressured a breakage in the floor layer around the drop and on the pool d. threw some water into the air (after the drop hit the floor) the sound waves hit your ears, the partitions, in spite of and have been the two bounced off or absorbed. The air itself absorbed lots of the sound power, heating it up ever so somewhat. The ripples bounced off the factors of the pond and moved returned and forth somewhat till the indoors viscosity of the water and the floor tension finally placed adequate drag on them. additionally any delicate stuff alongside the factors of the pond absorbed lots of the flexibility. Now, there is yet another rule (the 2d regulation of thermodynamics) in physics which says that power travels from a severe concentration to a low concentration, and that's strictly what happened. extremely of being concentrated on the drop, it unfold out over all the pond and area and became dissipated. good question. You controlled to conceal 2 considered necessary thermodynamics rules in one shot in a severe high quality relatively understood subject.