Question 1: A force F^→ = 75.8N is pulling on a box as shown. The box weighs at 198N, and was placed on a rough surface. At the contact, the static and kinetic friction coefficients are µ_s = 0.482 and µ_k = 0.412 respectively.

a) Please draw a free body diagram for the box; identify and label all forces; and select a coordinate system.

b) Please use your calculation to determine whether the force is sufficient to move the box. If it is not sufficient, what should be the minimum force to move the box? If it is sufficient, what is the magnitude of the box's acceleration?

Question 2: 150g of ice of initial temperature -10.0°C is stored in a container. Certain amount of water steam at initial temperature 100.0°C is directed into the container. After thermal equilibrium is reached, there is only water of temperature 50.0°C left in the container. Please determine how many grams of steam are used in this process. During the process, the ice-steam mixture loses 5.00 x 10³ J of heat to the container and the surroundings.

Question 3: A sphere of mass m = 0.348kg and radius r = 0.437m is spinning around its central axis as shown. If the kinetic energy of the sphere is 47.3 J, what is its angular speed?

Question 4: A stone is thrown up at an angle 34.7° above horizontal rind 5.41s later; it reaches the highest point of its trajectory. What is the magnitude of the launching velocity?