A chair with a mass of 20.0 kg is attached to one end of a frictionless pulley system via a
a strong massless rope. The other end of the rope is attached to a steel water tank sitting on a flat horizontal concrete surface (see the image to the right). The coefficient of static friction between steel and concrete is 0.45 and the coefficient of kinetic friction between the surfaces is 0.30. The water tank, which is full of water, has sprung a leak. The combined mass of the water and the tank is 500 kg. This mass slowly decreases as the water leaks from the hole. You (i.e. your entire mass) are sitting at rest in the seat. You and the seat will remain at rest as long as the force of static friction is strong enough to hold you.
LET [DOWN] and [RIGHT] be positive. Using your knowledge of physics, determine the following:
Draw the FBD of the system of you and the chair while at rest. Using the LET statement above, write out the net force equation. 
Draw the FBD of the system of the water tank at rest on the flat horizontal surface. Using the LET statement above, write out the net force equations for both the vertical and horizontal planes. 
Using the net force equations, determine the minimum mass of water that must be lost (i.e. leaked out) from the water tank in order for you and the seat to begin falling? 
As soon as the chair begins to move, static friction between the steel tank and concrete surface becomes kinetic friction. Determine the magnitude of the kinetic friction. 
Using Newton’s 2nd law, determine the acceleration of the system at the instant that the static friction becomes kinetic friction. 
4.2)Two books are accelerating to the right on a frictional surface and the coefficient of kinetic friction between the floor
ction between the floor and book is µk. Using the information given in the figure:
(a) draw free body diagrams for both the books, and also for the combined system (of mass m1+m2),
(b) find acceleration of the books along horizontal direction, and
(c) find the magnitude and direction of the force exerted by the left book on the right book.
3.A car of mass 1500-kg enters a circular path at point P and leaves at point Q (see the figure) at constant speed of 5.0m/s, and the frictional force acting on its tires is 2500-N.
a) how long it takes to reach point Q from point P, and
b) what should be the minimum value of the coefficient of static friction between the tires and the road?
4)In an elevator which is accelerating downward at 2.5ms−2 , a 25-kg block hangs from a spring attached to the ceiling of the elevator. If spring gets stretched by 0.15m, find its spring constant.
9.Use g = 9.8 m/s2.
The diagram below is a top-down view of two children pulling a 11.8-kg sled along the
ng the snow. The first child exerts a force of F1 = 11 N at an angle θ1 = 45° counterclockwise from the positive x direction. The second child exerts a force of F2 = 6 N at an angle θ2 = 30° clockwise from the positive x direction.
Find the magnitude (in N) and direction of the friction force acting on the sled if it moves with constant velocity.
direction (counterclockwise from the +x-axis)
What is the coefficient of kinetic friction between the sled and the ground?
What is the magnitude of the acceleration (in m/s2) of the sled if F1 is doubled and F2 is halved in magnitude?
11.Two identical small metal spheres with q1 > 0 and |q1| > |q2| attract each other with a force of
nitude 57.1 mN when separated by a distance of 3.84 m .The spheres are then brought together until they are touching, enabling the spheres to attain the same final charge q.After the charges on the spheres have come to equilibrium, they spheres are separated so that they are again 3.84 m apart.Now the spheres repel each other with a force
of magnitude 15.988 mN.What is the initial charge q1 on the first sphere?
12.. A uniform cylinder of mass M and radius R is initially at rest on a rough horizontal surface. A
ght string is wrapped around the cylinder and is pulled straight up with a force T whose magnitude is 0.8 Mg. As a result, the cylinder slips and accelerates horizontally. The moment of
inertia of the cylinder is I = 12 MR2 and the coefficient of kinetic friction is 0.4.
a. On the diagram above show all the forces applied on the cylinder. b. Determine the linear acceleration a of the center of the cylinder. c. Determine the angular acceleration α of the cylinder.
d. Explain the difference in results of linear acceleration a and αR.