Answer:
The forward speed of the disk is 4.07 m/s
Explanation:
Step 1: Data given
Angle = 25 °C
Distance the disk has rolled = 3.0 m
Step 2= Calculate the initial energy
Since the disk is, at moment t=0, at rest and at a height we only have potential energy
Ei = m*g*h
⇒with E = the potential energy
⇒with m = the mass of the disk
⇒with g = 9.81 m/s²
⇒with h = the height = x*sin 25° = 3*sin25°
Ei = m*g*X*sin25
Step 3: Calculate the final energy
Ef = 1/2 (mv²) + 1/2 Iw²
Ef = 1/2 (mv²) + 1/2(mR²)(v/R)²
Ef = 1/2mv² + 1/4 mv²= 3/4 mv²
Step 4: The law of conservation of energy
Ei = Ef
m*g*X*sin25 = 3/4 mv²
g*X*sin25 = 3/4 v²
Step 5: Calculate v
v = √(4/3 * g*X sin25°)
v = √(4/3 * 9.81*3 sin25°)
v = 4.07 m/s
The forward speed of the disk is 4.07 m/s
