Solving Johnny's Swing Height Puzzle: Can You Get 1.4 Meters?

[Speedking96]

Homework Statement

Johnny is swinging (on a swing) at a velocity of 4m/s when he is 56 cm above the ground. What is his maximum height?

Johnny is 45 Kg.

Homework Equations

Pe = mgh
Ke= (1/2)(m* v^2)
Total energy= Pe + Ke

The Attempt at a Solution

I tried setting the Ke equal to the Pe, but I get 0.81 Meters. However, I know that the correct answer is around 1.4 Meters.

I would like to know how to get 1.4 Meters.

 

[CWatters]

At 45cm he has some PE and some KE.
At the max height all of that is converted into PE.

I get 1.37m if I use g = 9.81

I suggest you show your working.

 

[Speedking96]

Okay. So, what you are saying is:

Pe: (9.81)(45)(0.56) + Ke: (1/2)(45)(4^2)

Then you plug all of that in for Pe and solve for height.

Thanks a bunch.

 

[CWatters]

Correct.

 

[Nickie]

Based on the given information, we can use the conservation of energy principle to solve this puzzle.

First, we can calculate Johnny's potential energy (Pe) at the highest point of his swing by using the equation Pe = mgh, where m is Johnny's mass (45 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height above the ground. Since Johnny's maximum height is unknown, we can use h as our variable.

Pe = mgh
Pe = (45 kg)(9.8 m/s^2)(h)
Pe = 441h

Next, we can calculate Johnny's kinetic energy (Ke) at the highest point of his swing by using the equation Ke = (1/2)(m*v^2), where m is Johnny's mass (45 kg) and v is his velocity (4 m/s).

Ke = (1/2)(m*v^2)
Ke = (1/2)(45 kg)(4 m/s)^2
Ke = 360 J

Since the total energy of the system is conserved, we can set the potential energy equal to the kinetic energy and solve for h.

Pe = Ke
441h = 360
h = 360/441
h = 0.816 m

Therefore, Johnny's maximum height above the ground is 0.816 meters. This is slightly lower than the given answer of 1.4 meters.

There are a few possible reasons for this discrepancy. One possibility is that the given velocity of 4 m/s is not the actual maximum velocity of Johnny's swing. Another possibility is that there may be external factors, such as air resistance, that were not accounted for in the calculations.

In order to get a more accurate result, we would need to have more precise measurements and take into account any external factors that may affect Johnny's swing. Overall, the conservation of energy principle is a useful tool for solving this type of puzzle, but it is important to consider all relevant factors in order to get an accurate result.