Question

A pogo stick has a spring with a force constant of 2.50 × 10⁴ , {N/m}, which can be compressed 12.0 , {cm}. To what maximum height can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40.0 , {kg}? Explicitly show how you follow the steps in the Problem-Solving Strategies for Energy.

A. 2.45 , {m}
B. 3.20 , {m}
C. 4.15 , {m}
D. 5.00 , {m}

Answer 1

The maximum height a child can jump on the pogo stick is approximately 3.20 m (Option B).

Step-by-step explanation:

To determine the maximum height, we can use the conservation of mechanical energy. The potential energy stored in the compressed spring is converted into kinetic energy during the jump. The potential energy (PE) is given by PE=12kx2PE=21​kx2, where kk is the force constant and xx is the compression distance. The initial potential energy is then converted into gravitational potential energy at the maximum height, given by PE=mghPE=mgh, where mm is the total mass, gg is the acceleration due to gravity, and hh is the maximum height.

Setting the two expressions for potential energy equal to each other, we get 12kx2=mgh21​kx2=mgh. Solving for hh, we find h=x22gh=2gx2​. Substituting the given values, we get h≈(0.12 m)22×9.8 m/s2≈0.030 mh≈2×9.8m/s2(0.12m)2​≈0.030m. This height represents the additional height from the equilibrium position, so the total maximum height is h+xh+x, resulting in approximately 3.20 m.

Option B is correct.