Juggles the clown stands on one end of a teeter-totter at rest on the ground. Bangles the clown jumps off a platform 2.5 m above the ground and lands on the other end of the teeter-totter, launching Juggles into the air. Juggles rises to a height of 3.8 m above the ground, at which point he has the same amount of gravitational potential energy as Bangles had before he jumped, assuming both potential energies are measured using the ground as the reference level. Bangles' mass is 75 kg. What is Juggles' mass?

All of the PE from Bangles is transferred to Juggles, so if Juggles has mass x, then

(75)(9.8)(2.5) = (x)(9.8)(3.8)
x = 75*(2.5/3.8) = 49.3 kg

49.3

Well, it sounds like Juggles really got launched into the air! But before I reveal Juggles' mass, let's do some clown math!

We know that gravitational potential energy (PE) is calculated using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

Since Juggles rises to a height of 3.8 m and has the same amount of gravitational potential energy as Bangles had before jumping, we can equate their potential energies:

m Juggles * g * 3.8 = m Bangles * g * 2.5

We also know that Bangles' mass is 75 kg, so let's substitute that into the equation:

m Juggles * g * 3.8 = 75 kg * g * 2.5

The acceleration due to gravity (g) cancels out on both sides of the equation, so we can simplify it further:

m Juggles * 3.8 = 75 * 2.5

Now, let's solve for m Juggles:

m Juggles = (75 kg * 2.5) / 3.8

Calculating that out, we get:

m Juggles ≈ 49.34 kg

So, Juggles' mass is approximately 49.34 kg. That's one flying clown!

To solve this problem, we can apply the principle of conservation of energy. The total mechanical energy of a system remains constant if no external forces are acting on it. In this case, we can consider the system to be Juggles and Bangles on the teeter-totter.

Let's start by calculating Bangles' initial potential energy before he jumped. The formula for gravitational potential energy is:

Potential energy = mass × gravity × height

Given:
Mass of Bangles (m) = 75 kg
Height of platform (h) = 2.5 m

Potential energy of Bangles before he jumped = m × g × h

Potential energy of Bangles before he jumped = 75 kg × 9.8 m/s^2 × 2.5 m

Next, we know that Juggles rises to a height of 3.8 m and has the same amount of gravitational potential energy as Bangles had before he jumped.

Therefore, the potential energy of Juggles at the maximum height is equal to the potential energy of Bangles before he jumped.

Potential energy of Juggles at maximum height = Potential energy of Bangles before he jumped

We can use the same formula to calculate Juggles' potential energy at the maximum height and solve for his mass (m_j):

m_j × g × 3.8 m = 75 kg × 9.8 m/s^2 × 2.5 m

Solving for m_j:

m_j = (75 kg × 9.8 m/s^2 × 2.5 m) / (9.8 m/s^2 × 3.8 m)

m_j = (75 kg × 2.5 m) / 3.8 m

m_j ≈ 49.34 kg

Therefore, Juggles' mass is approximately 49.34 kg.

he doesn't have one

Yes