Juggles the clown stands on one end of a teeter-totter at rest on the ground. Bangles the clown jumps off a platform 2.7 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 70 kg. What is Juggles' mass?

hyjf

49.7 To solve this problem, we can use the principle of conservation of energy. We can equate the initial potential energy of Bangles to the final potential energy of Juggles.

The potential energy of an object is given by the equation: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

Let's calculate the initial potential energy of Bangles before he jumps off the platform:

PE_initial = m * g * h_initial

Given the mass of Bangles (m = 70 kg) and the height of the platform (h_initial = 2.7 m), we can substitute these values into the equation:

PE_initial = 70 kg * 9.8 m/s^2 * 2.7 m

Next, let's calculate the final potential energy of Juggles when he reaches a height of 3.8 m:

PE_final = m * g * h_final

We want to find Juggles' mass, so let's substitute this value into the equation and solve for m:

PE_final = m * 9.8 m/s^2 * 3.8 m

Since PE_initial is equal to PE_final, we can set these two equations equal to each other:

70 kg * 9.8 m/s^2 * 2.7 m = m * 9.8 m/s^2 * 3.8 m

Now, we can cancel out the acceleration due to gravity (g = 9.8 m/s^2) from both sides of the equation:

70 kg * 2.7 m = m * 3.8 m

Finally, we can solve for m by dividing both sides of the equation by 3.8 m:

m = (70 kg * 2.7 m) / 3.8 m

m =~ 49.05 kg

Therefore, Juggles' mass is approximately 49.05 kg.