School of Science and Engineering
Al Akhawayn University
Final Test
Phy1401 (Fall 2003)
Instructor: Dr. H. Darhmaoui
Date: December 17, 2003
1. A 0.400 kg particle slides on a horizontal, circular track 1.50 m in radius. It is given an initial speed of
8.00 m/s. After one revolution, its speed drops to 6.00 m/s because of friction.
(a) Find the energy lost due to friction in one revolution.
(b) Calculate the coefficient of kinetic friction.
(c) What is the total number of revolutions the particle makes before stopping?
2. A stone falls from rest from the top of a building. A second stone is thrown downward from the same
height 2.00 s later with an initial speed of 30.0 m/s. Both stones hit the ground at the same time. (Neglect
air friction).
(a) How high is the building?
(b) What is the velocity of each stone when it hits the ground?
3. A simple pendulum having a length of 2.23 m and a mass of 6.74 kg is given an initial speed of 2.06
m/s at its equilibrium position. Assume it undergoes simple harmonic motion and determine its
(a) Period
(b) Total energy
(c) Maximum angular displacement
4. A cube of wood 20 cm on a side and having a density of 0.65 103 kg/m3 floats on water.
(a) What is the distance from the top face of the cube to the water level? (i. e. the non immersed
height of the cube)
(b) How much lead mass has to be placed on the top of the cube so that the top surface of the cube is
just level with the water? (Assume its top surface remains parallel to the water’s surface, density
of water = 1000 kg/m3)
5. A constant force F is applied to a lawn roller in the form of uniform solid cylinder of radius R and
mass M (ICM = 1 MR2). If the roller rolls without slipping on the horizontal surface, show that
(a) The acceleration of the center of mass is 2F/3M
(b) The minimum coefficient of friction necessary to prevent slipping is F/(3Mg).
6. A steel rod 4.0 cm in diameter is heated so that its temperature increases by 70 °C can then be fastened
between two grid supports. The rod is allowed to cool to its original temperature. Assume that the
Young’s modulus for the steel is 20.6 1010 N/m2 and its average coefficient of linear expansion is 11 10-6
(°C)-1, calculate the tension in the rod.
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School of Science and Engineering
Al Akhawayn University
7. A grinding wheel is in the form of a uniform solid disk of radius 7.00 cm and mass 2.00 kg. It starts
from rest and accelerates uniformly under the action of the constant torque of 0.600 Nm that the motor
exerts on the wheel.
(a) How long does the wheel take to reach its final speed of 1200 rev/min?
(b) Through how many revolutions does it turn while accelerating?
8. A wooden block of mass M = 2.00 kg resting on a frictionless horizontal surface is attached to a rigid
rod of length l= 0.50 m and of negligible mass. The rod is attached to a pivot (center of rotation) at the
other end. A bullet of mass m = 0.05 kg traveling parallel to the horizontal surface and perpendicular to
the rod with speed v = 150.0 m/s hits the block and gets embedded in it.
(a) What is the angular momentum of the bullet block system?
(b) What fraction of the original kinetic energy is lost in the collision?
9. A 3.0 kg mass starts from rest and slides a distance d down a frictionless 30° incline, where it contacts
an unstressed spring of negligible mass. The mass slides an additional 0.20 m as it is brought momentarily
to rest by compressing the spring (k = 400 N/m). Find the initial separation d between the mass and the
spring.
10. A very large storage tank filled with water develops a small hole in its side at a point 16 m below the
water level. If the rate of flow from the leak is 2.5 10-3 m3/min, determine
(a) The speed at which the water leaves the hole.
(b) The diameter of the hole
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