Concept explainers
The double pulley shown has a mass of 15 kg and a centroidal radius of gyration of 160 mm. Cylinder A and block B are attached to cords that are wrapped on the pulleys as shown. The coefficient of kinetic friction between block B and the surface is 0.2. Knowing that the system is at rest in the position shown when a constant force P = 200 N is applied to cylinder A, determine (a) the velocity of cylinder A as it strikes the ground, (b) the total distance that block B moves before coming to rest.
Fig. P17.14
(a)
Find the velocity of cylinder A as it strikes the ground.
Answer to Problem 17.14P
The velocity of the cylinder A when it strikes the ground is
Explanation of Solution
Given information:
The mass of the cylinder A is
The mass of the block B is
The radius of the outer pulley is
The radius of the inner pulley is
The centroidal radius of gyration is
The coefficient of friction between the surface and the block B is
The constant force applied at cylinder A is
Calculation:
Consider the acceleration due to gravity is
Consider the radius of the outer pulley as
Consider the radius of the inner pulley as
Find the velocity in the outer pulley
Here, the angular velocity of the pulley is
Find the velocity in the inner pulley
Substitute
Find the distance of the outer pulley
Here, the number of revolutions in the pulley C is
Find the distance of the inner pulley
Substitute
The initial total kinetic energy at rest is zero.
Find the mass moment of inertia in the pulley C
Here, the mass in the pulley C is
Substitute 15 kg for
Find the total kinetic energy
Substitute 5 kg for
Substitute 250 mm for
When
Substitute 150 mm for
Show free-body diagram the block B as in Figure 1.
Resolve the vertical component of forces as follows;
Find the frictional force
Substitute 0.20 for
Apply the principle of work and energy for the cylinder A, the block B and the double pulley C as follows;
Substitute 200 N for P, 1 m for
Write the equation of work and energy for the system using the equation.
Substitute 0 for
Therefore, the velocity of the cylinder A when it strikes the ground is
(b)
Find the total distance the block B moves before coming to rest.
Answer to Problem 17.14P
The total distance travelled by the block B before coming to rest is
Explanation of Solution
Given information:
The mass of the cylinder A is
The mass of the block B is
The radius of the outer pulley is
The radius of the inner pulley is
The centroidal radius of gyration is
The coefficient of friction between the surface and the block B is
The constant force applied at cylinder A is
Calculation:
Refer part (a) for
Substitute
Substitute 150 mm for
Find the total kinetic energy
Substitute 5 kg for
At the final position, the system comes at rest.
The kinetic energy at rest is zero.
Apply the principle of work and energy for the block B as follows;
Here, the additional distance travelled by the block is
Substitute
Write the equation of work and energy for the system using the equation.
Substitute 132.3066 J for
Find the total distance
Substitute 0.6 m for
Therefore, the total distance travelled by the block B before coming to rest is
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