Thursday

July 24, 2014

July 24, 2014

Posted by **mymi** on Monday, October 24, 2011 at 8:03am.

I got the height by 16sin47=11.7 m

I tried putting the k.e and p.e equations equal......lost!

- Physics -
**Regan**, Wednesday, June 26, 2013 at 7:33pmStep 1: We know that energy is conserved... so we know that KE(initial)+ PE(initial)= KE(final)+ PE (final).

Step 2: Since the hoop is initially at rest at the top of the hill, KE (initial) is 0. And after the hoop travels down the hill, all the PE is converted to KE, so PE(final) is equal to 0. So now we have that PE(initial)=KE(final)

Step 3: Plug in the formulas for PE and KE. PE is equal to mass*gravity*change in height. KE in this problem is KE(rotational)+KE(transitional). KE(rotational)= (1/2)*moment of inertia*angular velocity^2. KE(transitional)= (1/2)*mass*velocity^2.

So know we have: m*g*change in height= (1/2)*I*w^2+ (1/2)*m*v^2

Step 4: angular velocity (w) is equal to tangential velocity divided by radius (v/r). So substituting in this value for w, we now have: m*g*change in height= (1/2)*I*(v/r)^2+ (1/2)*m*v^2

Step 5: The moment of inertia for a hoop is mass*radius^2. So substituting this in for I, we now have: m*g*change in height=(1/2)*m*(r^2)*(v/r)^2+ (1/2)*m*v^2

Step 6: Simplify the equation! Notice that all the terms are multiplied by a factor of m, so we can pull it out. Also notice that in the KE(rotational) term r^2 cancels out. So now we have: g*change in height= (1/2)*v^2+(1/2)*v^2

Step 7: Solve for change in height! We know that the slope is 16 meters. And the angle of the slope is 47. sin(theta)=(opposite/hypotenuse)... so the change in height is 16*sin(47). Plugging that in for change in height, we now have: g*16*sin(47)= (1/2)*v^2+(1/2)*v^2

Step 8: Plug in 9.8 for gravity and solve for v. We get that v= 10.7 m/s!!!!

Good Luck!!! :)

**Related Questions**

Physics - A 1-kg thin hoop with a 50-cm radius rolls down a 47° slope without ...

Physics - 15. [1pt] A thin hoop of radius r = 0.59 m and mass M = 9.2 kg rolls ...

physics - A thin steel hoop of weight W and radius r starts from rest at A and ...

Physics - A hoop starts from rest at a height 3.0 m above the base of an ...

Physics - A hoop of mass M = 3 kg and radius R = 0.5 m rolls without slipping ...

physics - A solid sphere of radius R is placed at a height of 32cm on a 15degree...

Physics - Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, ...

Physics - What is the final velocity of a hoop that rolls without slipping down ...

physics - What linear speed must a 0.0508-kg hula hoop have if its total ...

physics - What linear speed must a 0.0487-kg hula hoop have if its total kinetic...