Question

International film and TV legend Danny DeVito is seated atop a playground slide. The coefficient of kinetic friction is 0.30, and the slide is 20m long at an angle of 50 degrees above the horizontal.

a.) Use the work-kinetic energy theorem (no potential energies) to predict Danny's speed when he reaches the bottom of the slide.

b.)Use energy conservation (including potential energies) to predict Danny's speed when he reaches the bottom of the slide.

Answer 1

here,

the coefficient of kinetic friction , uk = 0.3

s = 20 m

theta = 50 degree

a)

let the speed at the bottom of slide be v

using Work-energy theorm

the net work done = change in kinetic energy

Wff + Wg = 0.5 * m * ( v^2 - u^2)

- uk * (m * g * cos(theta)) * s + m * g * ( s * sin(theta)) = 0.5 * m * (v^2 - 0)

- 0.3 * (9.81 * cos(50)) * 20 + 9.81 * ( 20 * sin(50)) = 0.5 * (v^2 - 0)

solving for v

v = 15 m/s

the speed at the bottom is 15 m/s

b)

let the speed at the bottom of slide be v

using conservation of energy

the energy lost due to friction = change in kinetic energy

Wff = 0.5 * m * ( v^2 - u^2) - m * g * s * sin(theta)

- uk * (m * g * cos(theta)) * s = 0.5 * m * (v^2 - 0) - m * g * ( s * sin(theta))

- 0.3 * (9.81 * cos(50)) * 20 = 0.5 * (v^2 - 0) - 9.81 * ( 20 * sin(50))

solving for v

v = 15 m/s

the speed at the bottom is 15 m/s