Two velocities, unknown: height, mass, theta HELP

In summary, the problem involves a block sliding down a ramp with two different sets of velocities at points A and B. The goal is to use conservation of mechanical energy to find the final velocity of the second trial. The equation used is gh(initial) + (v(initial)^2)/2 = gh(final) + (v(final)^2)/2, set up twice for each set of velocities. The difference in gravitational potential between A and B must be the same for both runs, implying that the difference in kinetic energy must also be the same. The problem does not involve the mass in the mechanical energy equation and there is no frictional force acting on the block. The next step is to find the difference in kinetic energy and the heights,
  • #1
rmunoz
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0

Homework Statement


A block is sent sliding down a ramp. Its speeds at points A and B are 1.85 m/s and 2.60 m/s, respectively. Next, it is again sent sliding down the ramp, but this time its speed at point A is 3.95 m/s. What then is its speed at point B?

(point a is logically higher on the ramp than point b)

Homework Equations



The goal of this one is to use conservation of mechanical energy to deduce the final velocity of the second trial. Heres what i have:

since this is clearly a problem that does not need to involve the mass in the mechanical energy equation, i set something up that should describe the motion and the change in kinetic energy of this object:

gh(initial) + (v(initial)^2)/2 = gh(final) + (v(final)^2)/2

This should be set up twice (once for each set of velocities, the second set containing an unknown velocity for vfinal.)

What I'm confused about is how the kinetic energy and work equations come into play if at all. There is clearly no frictional force acting on the block so the acceleration is constant. Where do i go from here? Anybody have a suggestion on how to tackle the heights or weather or not it is necessary to find those quantities? i assume it is but i could very well be wrong.
 
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  • #2
Consider the difference in gravitational potential (A to B) between the two runs.

Won't that necessarily be the same for both runs?

So doesn't that imply the difference in kinetic energy must also be the same?
 
  • #3
wow...thats deathly simple. As usual, the hardest problems take the least amount of time... if you know what your doing!
 

1. What is the relationship between velocity, height, mass, and theta?

The relationship between velocity, height, mass, and theta can be described by the projectile motion equation, which states that the vertical component of velocity is equal to the initial velocity multiplied by the sine of the launch angle (theta) and the horizontal component of velocity is equal to the initial velocity multiplied by the cosine of the launch angle. The height and mass of the object will also affect the velocity and trajectory of the object.

2. How can I calculate the two velocities with only information about height, mass, and theta?

To calculate the two velocities, you will need to use the projectile motion equation and solve for the vertical and horizontal components of velocity. You will also need to know the acceleration due to gravity, which is typically 9.8 m/s^2. Once you have all the necessary information, you can plug it into the equation and solve for the velocities.

3. Can I determine the two velocities without knowing the mass of the object?

Yes, it is possible to determine the two velocities without knowing the mass of the object. This is because mass does not directly affect the velocity in the projectile motion equation. However, knowing the mass of the object can be useful in determining other variables such as the kinetic energy and momentum of the object.

4. How does changing the launch angle (theta) affect the two velocities?

The launch angle (theta) has a significant impact on the two velocities. As the launch angle increases, the vertical component of velocity also increases, while the horizontal component decreases. This means that the object will travel higher and farther with a larger launch angle. Conversely, a smaller launch angle will result in a lower and shorter trajectory.

5. Can I use this information to calculate other variables, such as the time of flight or maximum height?

Yes, you can use the information about the two velocities to calculate other variables in projectile motion, such as the time of flight and maximum height. These variables can be found by using the kinematic equations of motion, which take into account the initial velocities, acceleration due to gravity, and the displacement of the object.

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