Can you do H3 and H4? Thank you! H Indicate on the drawing all the forces that a

Question

Can you do H3 and H4?

Thank you!

H Indicate on the drawing all the forces that are acting on the object as it is rolling down the incline. (Note: assume that the object is not sliding or slipping on the surface of the incline.) H2. Draw the +x-axis parallel to the incline and the +y-axis perpendicular and upward. Write down Newton's second law for the x- and y-directions and for rotation. Include all the forces. (Hint: Assume the object is rolling without sliding. Therefore the force of friction is what is making the object rotate. This is not the same force of friction involved in Project #3, Steps 6-7) H3. Solve the above equations for the translational acceleration of the object. H4. Use this expression for the acceleration and derive an expression for the speed of the object after going from position A to position B in the figure on page 2.

Explanation / Answer

For rolling without slipping,

for rotation,

torque = I alpha

r f = I (a/r)

f = I a / r^2

now along the incline,

m g sin(theta) - f = m a

m g sin(theta) - I a / r^2

m g r^2 sin(theta) = (m r^2 + I) a

a = m g r^2 sin(theta) / ( I + m r^2) ......Ans

H.4 : vf^2 - v0^2 = 2 a d

v = sqrt[ 2 m g r^2 sin(theta) (dAB) / ( I + m r^2)] ...Ans

m = mass of objject
r = radius

I = moment of inertia

dAB = distance between A and B

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