2 . A solid disk rotates in the horizontal plane at an angular velocity of 2.90

Question

2. A solid disk rotates in the horizontal plane at an angular velocity of 2.90 × 10-2 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.17 kg.m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?

A 30.5 kg monkey hangs from a spring suspended from the ceiling of an elevator. The spring constant is equal to 840 N/m. What is the magnitude of the elevator's acceleration when the spring is stretched 0.43 m?

4. A 24.0 g bullet strikes a 0.65 kg block attached to a fixed horizontal spring whose spring constant is 6.90 × 103 N/m and sets it into vibration with an amplitude of 21 cm. What was the speed of the bullet before impact if the two objects move together after impact?

5. A 1.20 kg box rests on a plank that is inclined at an angle of 69.0° above the horizontal. The upper end of the box is attached to a spring with a force constant of 20.0 N/m, as shown in the figure. If the coefficient of static friction between the box and the plank is 0.17, what is the maximum amount the spring can be stretched and the box remain at rest?

6. A spring that has a force constant of 850 N/m is mounted vertically on the ground. A block of mass 1.00 kg is dropped from rest from height of 1.00 m above the free end of the spring. By what distance does the spring compress?

7. The frequency of a simple harmonic oscillator is increased from 0.15 Hz to 0.45 Hz. What is the change in its period (final - initial)?

8. Students use a simple pendulum with a length of 36.5 cm to measure the acceleration of gravity at the location of their school. If the period of the pendulum is 1.27 s, what is the experimental value of (g) at the school?

9. To measure the static friction coefficient between a 1.10-kg block and a vertical wall, a spring (k = 700 N/m) is attached to the block, is pushed on the end in a direction perpendicular to the wall until the block does not slip downward (see figure). If the spring is compressed by 0.044 m, what is the coefficient of static friction?

10. A 27.0-kg block is resting on a flat horizontal table. On top of this block is resting a 13.0-kg block, to which a horizontal spring is attached, as the drawing illustrates. The spring constant of the spring is 310 N/m. The coefficient of kinetic friction between the lower block and the table is 0.490, and the coefficient of static friction between the two blocks is 0.720. A horizontal force is applied to the lower block as shown. This force is increasing in such a way as to keep the blocks moving at a constant speed.

Determine the amount by which the spring is compressed at the point where the upper block begins to slip on the lower block.

Explanation / Answer

1)

T= tsnion in the cable

L = length of the beam.

Apply net torque about one end = 0

T*L*sin(90 - 41) - m*g*(L/2)*sin(90-41) = 0

T = m*g/2

T = 110*9.8/2

T = 539 N

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