A mass of 11 kg is being pushed up a frictionless incline with a constant force of 35 Newtons directed parallel to the incline, up the incline. At the top of the incline the mass is moving at 29 m/s up the incline. If the angle of inclination is 59 degrees and the height (not length) of the incline is 23 meters, what was the magnitude of the mass's velocity at the bottom of the incline in m/s?
Vf = (29m/s,59deg).
Yf = ver. = 29sin59 = 24.85m/s. = Vertical component.
Yf^2 = Yo^2 + 2g*d,
Yo^2 = Yf^2 - 2g*d,
Yo^2 = (24.85)^2 - 19.6*23 = 166.7,
Yo = 12.9m/s. = Ver. component of initial velocity.
Vo = Yo / sin59=12.9 / sin59=15.1m/s. =
Initial velocity.
A mass of 18 kg is being pushed up a frictionless incline with a constant force of 20 Newtons directed parallel to the incline, up the incline. At the top of the incline the mass is moving at 23 m/s up the incline. If the angle of inclination is 58 degrees and the height (not length) of the incline is 24 meters, what was the magnitude of the mass's velocity at the bottom of the incline in m/s?
To find the magnitude of the mass's velocity at the bottom of the incline, we need to use the principles of conservation of energy.
First, let's find the potential energy of the mass at the top of the incline. The potential energy can be calculated using the formula:
Potential energy = mass * gravity * height
In this case, the mass is 11 kg, gravity is 9.8 m/s², and the height is 23 meters. So, the potential energy at the top of the incline is:
Potential energy = 11 kg * 9.8 m/s² * 23 meters
Next, let's find the kinetic energy of the mass at the top of the incline. The kinetic energy can be calculated using the formula:
Kinetic energy = 0.5 * mass * velocity²
In this case, the mass is 11 kg, and the velocity is given as 29 m/s. So, the kinetic energy at the top of the incline is:
Kinetic energy = 0.5 * 11 kg * (29 m/s)²
Now, since there is no energy lost due to friction, the total energy at the top of the incline (potential energy + kinetic energy) is equal to the total energy at the bottom of the incline.
So, the total energy at the bottom of the incline is:
Potential energy at the bottom + Kinetic energy at the bottom
Since the height at the bottom is 0 and the velocity at the bottom is what we need to find, the potential energy at the bottom is 0:
Potential energy at the bottom = 0
Thus, the total energy at the bottom is:
Total energy at the bottom = Kinetic energy at the bottom
Finally, let's calculate the kinetic energy at the bottom of the incline using the formula mentioned earlier:
Kinetic energy = 0.5 * mass * velocity²
We can rearrange the formula to solve for the velocity at the bottom:
velocity at the bottom = √ (2 * Kinetic energy / mass)
Now, substitute the mass and kinetic energy values into the equation:
velocity at the bottom = √ (2 * (Potential energy at the top + Kinetic energy at the top) / mass)
Calculate the Potential energy and Kinetic energy at the top using the formulas mentioned earlier.
Finally, substitute the calculated values into the equation, and you will get the magnitude of the mass's velocity at the bottom of the incline in m/s.