Question

In a Coyote/Road Runner cartoon clip, a spring expands quickly and sends the coyote into a rock. If the spring extended 5 m and sent the coyote of mass 20 kg to a speed of 15 m/s,

(a) what is the spring constant of this spring?
(b) If the coyote were sent vertically into the air with the energy given to him by the spring, how high could he go if there were no non-conservative forces?

Answer 1

The spring constant of the spring is 1800 N/m. If the coyote were sent vertically into the air, it could reach a maximum height of approximately 11.47 meters with no non-conservative forces acting.

Step-by-step explanation:

To find the spring constant (k) of the spring that sends the coyote into the rock, we can use the work-energy principle. The work done by the spring is equal to the kinetic energy gained by the coyote:

Work = (1/2)mv² = (1/2)kx²

Where m is the mass of the coyote, v is the velocity, k is the spring constant, and x is the extension of the spring. Using the given values (m = 20 kg, v = 15 m/s, x = 5 m), we can solve for k:

k = (mv²)/(x²) = (20 · 15²)/(5²) = 1800 N/m

For part (b), if the coyote were sent vertically into the air, we can use the conservation of energy to find the maximum height (h):

Potential Energy at maximum height = Kinetic Energy given by the spring

(mgh) = (1/2)mv²

h = (v²)/(2g) = (15²)/(2 · 9.8) ≈ 11.47 m

The coyote could reach a maximum height of approximately 11.47 meters.