Simple mechanical energy question [gr.11]

In summary, the conversation discusses a simple mechanical energy question involving children playing in the jungle and using a rope to swing from a tree limb. The question asks for the maximum height a 40 kg child reaches and the speed a 30 kg child would have to run to reach the same height. The summary provides the equation used to solve for maximum height, which is found to be 3.27m. For the second question, the summary shows how to solve for the speed, which is found to be 7.999 m/s. The conversation also explains why the same speed is needed for both children to reach the same height.
  • #1
kassy_in_the_sky
5
0
[urgent] simple mechanical energy question [gr.11]

Several children, pretending they are playing in the jungle, suspend a rope from an overhead tree limb. A child of mass 40 kg running at 8.0m/s grabs the rope and swings off the level ground.

a) What maximum height does the child reach?
b) How fast would a 30 kg child have to run to reach the same height as the 40 kg child?


½mv1²+mgh1 = ½mv2²+mgh2

a) m=40kg, v1=8.0m/s, h1=0m, g=9.8m/s², v2=0m/s (at max height v=0)

h2=?

½mv1²+mgh1 = ½mv2²+mgh2

½mv1²= mgh2

h2 = 3.27m = 3m (is this correct?)

im really confused with B... coz i got 8m/s... it doesn't make sense to me how they can run at the same speed and achieve the same height??!

this is really urgent... so please help me! >_< thanks!
 
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  • #2
A)
I would say: the KE at the point of him grabbing it = the PE at his peak(all his KE has become PE) so KE=PE so ½mv²=mgh substituting:
.5*40*8²=40*9.8*h
1280=392h
h=3.265m

B)change 30 for 40 above and v is unknown
.5*30*v²=30*9.8*3.265
15v²=959.91
v²=63.994
v=7.999m/s

yes, it is the SAME v for both! Why? because the m cancels out on both sides of the equation: the m in ½mv² and the m in mgh divide out!
 
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  • #3
thank you! ^^
 

1. What is simple mechanical energy?

Simple mechanical energy is the energy possessed by an object due to its motion or position. It can be either kinetic energy, which is the energy of motion, or potential energy, which is the energy stored in an object's position.

2. How is simple mechanical energy calculated?

The formula for calculating simple mechanical energy is E = KE + PE, where E is the total energy, KE is the kinetic energy, and PE is the potential energy. Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. Potential energy is calculated using the formula PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

3. Can simple mechanical energy be converted into other forms of energy?

Yes, simple mechanical energy can be converted into other forms of energy. For example, when a ball is thrown, its kinetic energy is converted into potential energy as it reaches its maximum height. When the ball falls back down, the potential energy is converted back into kinetic energy.

4. What are some examples of simple mechanical energy?

Some examples of simple mechanical energy include a swinging pendulum, a rolling ball, a stretched rubber band, a falling object, and a compressed spring. Any object that is in motion or has the potential to move has simple mechanical energy.

5. How does friction affect simple mechanical energy?

Friction can decrease the amount of simple mechanical energy in a system by converting it into heat energy. For example, when a ball rolls on the ground, some of its kinetic energy is lost due to friction with the surface, causing it to slow down. Similarly, a swinging pendulum will eventually come to a stop due to the friction in the air and at the pivot point.

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