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A motor exerts torque on a carousel for it to attain a speed of 2.5 rev/s starting from rest in 3.5 s. Find the work done by the motor if the carousel has a radius of 27 m and mass of 1.75 x10^5kg. Consider
the carousel to be a thin-walled cylinder rotating about its center.
Four identical spheres of masses 2.0 kg each and radius 0.25 m are situated at the four corners of a square. One side of the square measures 3.00 m. Find the moment of inertia about an axis (a) passing through the center of the square and perpendicular to its plane, (b) passing through one of the masses and perpendicular to its plane, (c) passing through two adjacent masses parallel to the plane, and (d) in the plane running diagonally through two meters.
2. Block 1 and block 2, with masses m1 = 5kg and m2 = 2kg, are connected by a system of massless, inextensible ropes and massless pulleys as shown in Fig. 2. (a) (Marks: 2) Draw the complete free body force diagram of the system. (b) (Marks: 4) Solve for the accelerations of block 2 and block 1. Assume that downward direction is positive. (c) (Marks: 2) Calculate the tensions in each rope
1. Block 1 of mass m1 = 2 kg is placed on block 2 of mass m2 = 3 kg which is then placed on
a table. A string connecting block 2 to a hanging mass M passes over a pulley attached to one
end of the table, as shown in Fig. 1. The mass and friction of the pulley are negligible. The
coefficients of friction between block 1 and block 2 are /1s = 0.2, M1k = 0.1 and between block
2 and the tabletop are 42s = 0.3, Mzk = 0.15.
(a) Draw the complete free body diagram of the system and determine the largest
value of M for which the blocks can remain at rest.
(b)Now suppose that M
= 2.5 kg which is large enough so that the hanging block
descends and block 1 slips on block 2. Draw the complete free body diagram of the system and
determine each of the followings.
I. The magnitude a of the acceleration of block 1
it. The magnitude ay of the acceleration of block 2
A 3.56 kg block resting on a smooth horizontal surface is attached to a string that passes over a frictionless pulley as shown in the figure. The pulley has a radius of 0.28 m. A force of 7.5 N pulls the other end of the string. As a result, the block moves a distance of 0.2 m starting from rest. Find the (a) acceleration of the block, (b) angular acceleration of the pulley, and (c) moment of inertia of the pulley.
Joana Marie is a swimmer. She swims directly across a river flowing at 4 m/s with a velocity of 2 m/s. What will be the actual velocity of Joana Marie relative to the river? Determine its angle.
Daisy is running 5 m/s due East while crossing with Joel who is running 4 m/s due North. What is Daisy's actual velocity and angle relative to Joel's?
Arlene is stationary relative to the ground. Aiza is riding toward Arlene on her e-bike 5 m/s relative to the ground. Aiza throws a water balloon forward at 3 m/s relative to the e-bike. With what speed does it strike Arlene?A simple pendulum takes 23.5 seconds to complete 20 cycles. What is the period (T) and frequency of the pendulum?
The moon is 3.9 × 105 km from Earth's center and 1.5 × 108 km from the Sun's center. The masses of earth and the sun are 6.0 × 1024 kg and 2.0 × 1030 kg, respectively. Find the ratio of the gravitational fields due to Earth and the Sun at the center of the Moon.
