For the following questions, assume the potential
energy of the mass was 0.20 J when released at
point E.
a) If the mass-cord system loses 0.20 J of potential
energy as it travels to point C, what velocity would it
gain as it is accelerated to point C?
b) If all this kinetic energy was converted to
gravitational potential energy at its maximum height
at A, how far is point A above point C?
a) To solve this problem, we can use the principle of conservation of energy. The initial potential energy at point E is given as 0.20 J. The potential energy lost as the mass-cord system travels to point C is also given as 0.20 J. This potential energy loss is converted into kinetic energy gained by the mass.
To find the velocity gained at point C, we can equate the potential energy loss to the kinetic energy gained using the formula:
Potential Energy Loss = Kinetic Energy Gained
0.20 J = (1/2) * m * v^2
where m is the mass of the object and v is the velocity gained at point C.
Since the mass is not given, we cannot directly solve for the velocity. We need additional information to determine the mass.
b) To find the height difference between point A and point C, we can start by using the principle of conservation of energy again. We know that all the kinetic energy gained at point C is converted into gravitational potential energy at point A.
The kinetic energy gained at point C is given by:
Kinetic Energy Gained = (1/2) * m * v^2
This kinetic energy is converted into gravitational potential energy at point A, which can be calculated using the formula:
Gravitational Potential Energy = m * g * h
where g is the acceleration due to gravity (9.8 m/s^2) and h is the height difference between point A and point C.
Setting these two expressions equal to each other, we can solve for h:
(1/2) * m * v^2 = m * g * h
Simplifying the equation, we find:
v^2 = 2 * g * h
Now, we can isolate h and solve for it:
h = v^2 / (2 * g)
Substituting the known values, we can find the height difference between point A and point C.
I can not see your drawing f course but assume that point C is below point E
It lost 20 Joules dropping from E to C
Its velocity at E was zero
drop in PE = gain in Ke
20 = (1/2) m v^2
so
v = sqrt(40/m)
If it gains 20 Joules of PE going back up and losing that 20 Joules of KE then point A is at the same height as point E
If you drop on your sled from the top of a hill then if the snow is frictionless you have enough kinetic energy at the bottom to make it up the next hill to the same height.