problem 1: If the coefficient of friction between a box and the bed of a truck is µ, Wfind out the maximum acceleration with which the truck can climb a hill, making an angle µ with the horizontal, without the box’s slipping on the truck bed?

problem 2: During the take-off of an airplane, a passenger removes his tie and lets it hang loosely from his fingers. He observes that during the take-off run, which last 30 seconds, the tie makes an angle of 15⁰ with the vertical. Suppose that the runway is level. What is the speed of the plane at takeoff and how long the runway is needed?

problem 3: A particle of mass m moves in the field of a repulsive central force F(r) = Am/r³, where A is a constant. At a very large distance from the force center the particle has speed v₀ and its impact parameter is b. Show that the closest m comes to the center of force is given by r_min = (b + A/v_o).

problem 4:

a) Prove that the time average of the potential energy of a planet in an elliptical orbit having a semi-major axis a about the sun is –k/a, while the potential energy at a distance r is V(r)= –k/r.

b) Compute the time average of the kinetic energy of the planet

problem 5: Show that the period of a physical pendulum is equavalent to T = 2π√(d/g)

where d is the distance between the point of suspension O and the center of oscillation O’.

problem 6: A billiard ball of radius a is initially spinning about a horizontal axis with angular speed ω₀ with zero forward speed. If the coefficient of sliding friction between the ball and the billiard table is before sliding ceases to occur.