4. A solid sphere with mass of 2.5 kg, and radius of 20 cm rolls down an plane,

Question

4. A solid sphere with mass of 2.5 kg, and radius of 20 cm rolls down an plane, inclined at an angle of 15. (Moment of inertia for a solid sphere is given by MR2 (a) What is the acceleration of the sphere as it rolls down the plane? (b) Assuming the sphere starts from rest, calculate the final velocity of the sphere fter it travels 1 m. (Hint: Use trigonometry to calculate h for the sphere.) (c) If a block slid down a frictionless incline plane, inclined at an angie oition of energy of 15, would it move faster or slower than the solid sphere? Explain your answer in terms of conservation of

Explanation / Answer

Kinetic energy of rolling object = mv2(1+I/mr2 ) / 2   where I is moment of inertia
Decrease in potential energy = mg (delta h) = mg l sin theta, where l is linear distance travelled
mv2 (1+I/mr2 )/ 2 = mg l sin theta
v2 = 2 g l sin theta / (1+I/mr2 ) .......1
Comparing it to v2 = 2 a l for object atrting from rest
accelration of object rolling down the plane, a = g sin theta / (1 + I/mr2)
a = g sin theta / ( 1+2/5)
= 4.9 m/sec2

b) From equation 1, v2 = 2 g l sin theta / (1+2/5 )
                                   = 9.9 m/s
c) Kinetic energy of block = mv2/2
So v2(block) = 2 g l sin theta ...2
from 1 and 2 we need to compare sin15 with sin 45 / (7/5) to compare speed of block with sphere
sin15 = 0.26
sin 45 / (7/5) = 0.5
Hence block will move at slower speed compared to sphere.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

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