A 145 kg box is placed on a frictionless incline with an angle of 22.0° above the horizontal. The box slides at constant velocity down the incline as you push it. Determine the magnitude of the force you apply on the box if the force is parallel to the horizontal.

Two trucks are pulling a large storage container north, as shown in the figure below. The sum of the forces $\overrightarrow{F_1}$ and $\overrightarrow{F_2}$ that are exerted on the container by the horizontal steel cables in the north direction are also parallel to line "L". Note that $\overrightarrow{F_1}$ = 4400 N. Calculate $\overrightarrow{F_2}$ and the magnitude of $\overrightarrow{F_1}$ + $\overrightarrow{F_2}$ .

A container being lowered from a crane is held in place by a light steel cable that makes an angle of 58.0° from the vertical and a horizontal synthetic cable. If the container has a mass m = 4520 kg, determine
a) The tension T₁ in the slanted cable.
b) The tension T₂ in the horizontal cable.

Two physics enthusiasts devise an experiment in which a 40-centimeter-long thread suspends a bar magnet(m = 10g). When another bar magnet is brought close to the first one with the identical poles facing each other (north to north or south to south),  they repel one another. If the second magnet is held in place it causes the hanging magnet to swing out to a 15-degree angle and remain there. Determine the magnitude of the magnetic force that causes the repulsion between magnets (making it swing).

A weightlifter is engaging in a workout routine, aiming to lift a 95-kg iron block with the aid of a rope, as depicted in the figure. Determine the necessary downward force, represented as $\overrightarrow{F}$, that the weightlifter must exert to ensure the rope sags at its midpoint by 1.8 m.

A 1200kg stalled truck on a level parking lot is pushed by a small SUV of mass of 650 kg in a direction due north. The SUV is pushing on the truck with a 2200 N horizontal force. Determine the magnitude of the force applied to the SUV by the truck. 

A 120 kg motorcycle in a remote village pulls on a 200 kg cart. The cart is secured to the motorcycle using a hook. During take-off, the rear tyre exerts a 90 N horizontal force against the gravel road. Determine the magnitude of the force exerted by the motorcycle on the cart. Ignore rolling friction.

A researcher with a mass of 82.0 kg (including a gun) stands on a frictionless wet ground holding a gun. The researcher fires a 25 g bullet horizontally. The bullet acquires a speed of 650 m/s in 1.20 s. Determine the rebound velocity of the researcher, assuming a constant force on the bullet.

The figure depicts an arrangement in which a block of 5.0 kg is connected to a block of 1.5 kg through massless and frictionless pulleys. Calculate the magnitude of the acceleration of the upper box.

A 40-kg monkey is sitting high in the trees. A woody vine hangs from a nearby tree branch to the bottom of the trees. However, it can only support a mass of 30 kg. How should the monkey climb down the vine so it doesn't break? (Suggest quantitatively.)

A student hangs two balls by a string, from a pulley connected with the roof of his house, as shown in the figure below. In the beginning, both the two balls are stationary at a height of 1.2 m from the ground. While the frictionless pulley of negligible mass is 5.2 m above the ground. Calculate the maximum height the lighter ball reaches if the system moves freely. 

[Hint: Evaluating the lighter ball's acceleration, calculate its speed when the other ball touches the ground. Think of it as its "launch" speed. Presume the balls don't collide with anything and the mass of the string is negligible.]