1. Imagine a landing craft approaching the surface of Callisto, one of Jupiter's moons. If the engine provides an upward force (thrust) of 3260 N, the craft descends at constant speed; if the the engine provides only 2200 N, the craft accelerates downward at 0.39 m/s2.
    • a.) What is the weight of the landing craft in the vicinity of Callisto's surface?
    • b.) What is the mass of the craft?
    • c.) What is the free-fall acceleration near the surface of Callisto?

  2. .
    A 10 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 15 kg package on the ground.
    • a.) What is the magnitude of the least acceleration the monkey must have if it is to lift the package off the ground?

      If, after the package is lifted, the monkey stops its climb and holds onto the rope, what are

    • b.) its acceleration?

    • c.) the tension in the rope?

  3. .
    An elevator operates by having a passenger cage (labeled A in the figure below) attached to a pulley, a driving mechanism (labeled C), another pulley, and a counterweight (labeled B). In operation, mechanism C grabs the cable, either forcing it along or retarding its motion. This process means that the tension TA in the cable attached to the passenger cage does not have to be the same as the tension TB attached to the counterweight. Suppose the upward acceleration of A and the downward acceleration of B have the magnitude a = 2.0 m/s2. The mass of the elevator cage is 1100 kg and the mass of the counterweight is 1000 kg. Neglecting the pulleys and the mass of the cable, find

    • a.) the tension TA

    • b.)the tension TB

    • c.) the force on the cable produced by C.

  4. In the systems shown below, the magenta object is a scale that measures the tension in the massless, stretchless rope. Determine the force in newtons registered by the scale for each scale.
    • a.)
    • b.)
    • c.) Optional: If you want a challenge, try doing part b. for the case in which one of the masses is 7 kg while the other remains at 5 kg. Warning: this now becomes a quite challenging problem.

  5. .
    • a.) Find the acceleration of masses m1 and m2 for the figure shown below. The pulleys are massless and all surfaces are frictionless.

    • b.) What do these results predict in the limits m2 >> m1 and m1 >> m2?

  6. .
    Two masses m1 and m2 sit on a frictionless, horizontal surface and are connected by a massless, stretchless string. A force F is applied to block m2 as shown in the figure below. Find the following:

    • a.) the acceleration of block m1

    • b.) the tension T, in the string between the blocks
  7. Three blocks with masses m1 < m2 < m3 are on a level frictionless surface as shown in the figure below.

    A force F pushes the blocks to the right.

    • a.) Determine the direction and magnitude of all the forces acting on each block (Note: the magnitudes need to be in terms of F, the masses, and the gravitational acceleration, g).
    • b.) Which block experiences the greatest net horizontal force? Which block experiences the greatest net horizontal force if blocks m1 and m3 are interchanged (i.e. switch places)?

  8. .
    Repeat problem 6 for the case in which friction exists between the blocks and the horizontal surface exists. You may assume that the blocks are in constant motion and that the coefficient of kinetic friction between the blocks and the surface is mk.

  9. .
    Repeat problem 7 with the coefficient of kinetic friction is mk. You can assume that the blocks are in constant motion.

  10. Two blocks with masses m1 = 5 kg and m2 = 10 kg are situated as shown in the figure below.

    The coefficients of static and kinetic friction between the blocks and block m2 and the table are ms = 0.3 and mk = 0.1, respectively. The rope is massless and stretchless.

    • a.) Find the minimum magnitude of force F necessary to initiate motion of m2.
    • b.) Determine the tension in the rope and the acceleration of each block if F = 45.0 newtons.

  11. .
    Determine the amount of force that must be applied by the person in the following scheme to lift herself and the platform assuming that the total mass of pulley, platform, and person is M.

  12. .
    For the half-Atwood machine shown in the figure below, the coefficient of kinetic friction between the table and block m2 is mk = 0.2. If the masses are m2 = 2 kg and m1 = 5 kg, determine the tension in the string connecting them.

  13. A weight lifter stands on a bathroom scale while pumping a barbell up and down. What happens to the reading on the scale as this is done? Suppose the weightlifter actually throws the barbell upward. How does the reading on the scale change through the throwing motion?

  14. .
    The figure below shows three blocks with masses m2 = 5 kg and m3 = 4 kg. The coefficient of static friction between the blocks and m2 and the table is ms = 0.2. What is the maximum mass m1 can be if no blocks are to move? Find the tension in the string attached to m3 for this maximum value of m1.

  15. .
    Find the acceleration of mass m1 if the coefficient of kinetic friction between m2 and m3 is 0.1. Use the values of the masses given in problem 14.