You pull on a string with a horizontal force of magnite Fyb 62 N that is attache
ID: 2304594 • Letter: Y
Question
You pull on a string with a horizontal force of magnite Fyb 62 N that is attached to a block of mass mb- 7.8 kg, then to the axle of a solid cylinder of mass me- 4.1 kg and radius r- 0.4 m, then to a spring of spring constant k = 170 N/m. This is all done on an inclined plane where there is friction ??4-0.66 and k-0.32), and the incline angle is 31 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. yb First, what is the speed of the block and cylinder after you have pulled the block and cylinder 111 cm down the plane? v1.584 m/s 1pts Submit Answer Incorrect. Tries 7/15 Previous Tries jsMathExplanation / Answer
Solution:
A) energy due to friction = ((m_b*g*cos(theta)-Fsin(theta))*u*d
= (7.8 *9.8 *cos31 - 62sin31) * 0.32 * 1.11
= 11.93 J
Kinetic translational for both the cylinder and the block = 0.5 * 11.9 * v2
= 5.95 * v2
Kinetic rotational for the cylinder = 0.25 * 4.1 * v2
= 1.025 * v2
The change in potential energies of both the cylinder and the block = -m*g*dsin(theta)
= - 11.9 * 9.8 *1.11*sin31
= - 66.67 J
spring potential energy = 0.5 * 170 * 1.11 * 1.11
= 104.73 J
11.93 + 5.95 * v2 + 1.025 * v2 - 66.67 + 104.73 = 62 * cos31 * 1.11
=> 6.975* v2 = 9.00
=> v = 1.136 m/sec ----------------------> speed of the block and cylinder
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