1. Compare a hockey puck (assumed perfect rigid solid cylinder with radius R, ma

Question

1. Compare a hockey puck (assumed perfect rigid solid cylinder with radius R, mass M, and thickness d) sliding down a hill without friction with one on its edge rolling down a hill like a wheel without slipping (with friction to make the wheel roll). Assuming the puck starts out at height H in both cases, what is the final translational velocity of the puck at the bottom of the hill? Derive the formula for the final translational velocity in both cases using g for earth's acceleration of gravity. Which case has a higher final translational velocity: sliding without friction or rolling without slipping? Why is this

Explanation / Answer

2] When there is sliding without friction,

In order to perform a loop, the minimum velocity at the top of loop should be such that,

mv^2/RL = mg

0.5mv^2 = 0.5 mg RL

so by energy conservation, mgH = mg2 RL + 0.5 mv^2

mgH =  mg2 RL + 0.5 mg RL = 2.5 mg RL

H = 2.5 RL answer

When rolling without slipping,

In order to perform a loop, the minimum velocity at the top of loop should be such that,

mv^2/(RL -R-D) = mg

0.5mv^2 = 0.5 mg (RL -R-D)

so by energy conservation, mgH = mg(2 RL- R-d)+ 0.5 mv^2 + 0.5 I w^2

mgH = mg(2 RL- R-d)+ 0.5mg(RL -R-d)+ 0.5 I w^2 where I = M(R+0.5d)^2, w = v/(R+d)   

mgH = mg(2 RL- R-d)+ 0.5mg(RL -R-d)+ 0.5m(R+0.5d)^2*v^2/(R+d)^2

mgH = mg(2 RL- R-d)+ 0.5mg(RL -R-d = )+ 0.5 mg (RL -R-d)(R+0.5d)^2/(R+d)^2

H = (2 RL- R-d)+ 0.5(RL -R-d)+ 0.5(RL -R-d)(R+0.5d)^2/(R+d)^2

if d is negligible,

H =  (2 RL- R)+ (RL -R)

H = 3RL- 2R

If R is also negligible as compared to radius of loop,

  H = 3RL

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.