1. a little spider monkey named flo has stolen a bunch of bananas from her older brother Charley and is now running away frm him with the bananas in hand. She sees salvation in a long vine and grabs the bottom, hoping to swing away
a) if she has a mass of 5.3kg and the bananas with a mass of 0.5 kg reaches a height of 1.2 m before slowing to a stop and swinging back down, how fast was she running when she grabbed the vine?
b) As she swings back down charley (whose mass is 5.9kg) is standing just at the bottom of the swing.. He grabs her and swings her up together. What height will the two monkeys and the coveted banana reach?
c) As a result of their fighting they happen to drop the bananas just as the vine pendulum reaches this new height. How fast will the two monkeys be moving when they let go off the vine at the bottom again?
And your work is where? You are posting "urgent" problems under different names. Very suspicious, we really frown on cheating.
ok so i solved for 1a) first i used the ep=mgh formula to get 68J then i plugged that in the Ek=1/2 mv^2 formula and got 4.8 m/s
but i'm stuck on b) and c) can u please help
To solve these physics problems, we can make use of conservation of energy and Newton's laws of motion.
a) Let's first calculate the potential energy gained by Flo and the bananas when they reach a height of 1.2 m. The formula for potential energy is:
Potential Energy = mass * gravity * height
The mass of Flo and the bananas combined is: 5.3 kg + 0.5 kg = 5.8 kg
The acceleration due to gravity is approximately 9.8 m/s².
Potential Energy = 5.8 kg * 9.8 m/s² * 1.2 m = 68.016 J
Since energy is conserved, this potential energy must be equal to the kinetic energy Flo had when she grabbed the vine. The formula for kinetic energy is:
Kinetic Energy = 0.5 * mass * velocity²
Where velocity is the speed at which Flo was running. Rearranging the formula, we can solve for velocity:
velocity = √(2 * (Potential Energy / mass))
velocity = √(2 * (68.016 J / 5.3 kg)) ≈ 4.11 m/s
Therefore, Flo was running at a speed of approximately 4.11 m/s when she grabbed the vine.
b) When Charley grabs Flo and they swing together, they still conserve their total mechanical energy. The potential energy gained at the highest point will be equal to the initial kinetic energy.
At the highest point, all of the energy will be in the form of potential energy. Therefore:
Potential Energy = Kinetic Energy
At the highest point, all energy has been converted from kinetic energy to gravitational potential energy. So, we can write:
Potential Energy = (mass of Flo + mass of Charley + mass of bananas) * gravity * height
Plugging in the given values:
Potential Energy = (5.3 kg + 5.9 kg + 0.5 kg) * 9.8 m/s² * height
The height is not given in this part of the question, so you need to provide that information in order to calculate it accurately.
c) After dropping the bananas, Flo and Charley are still swinging on the vine. At the lowest point, all of their potential energy will be converted back to kinetic energy.
Kinetic Energy = Potential Energy
Using the same formula as in part a:
Potential Energy = (mass of Flo + mass of Charley) * gravity * height
Plugging in the given values:
Potential Energy = (5.3 kg + 5.9 kg) * 9.8 m/s² * height
The height is the same as in part b, so you can use the calculated value. Once you have the potential energy, you can solve for the final velocity using the same formula as in part a:
velocity = √(2 * (Potential Energy / (mass of Flo + mass of Charley)))
Substitute the values and you will get the final velocity of Flo and Charley when they let go of the vine.