6. Intro to Forces (Dynamics)

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. Draw two free-body diagrams: one for each block.

II) Using focused laser light, optical tweezers can apply a force of about 10 pN (piconewtons) to a 1.0-μm-diameter polystyrene bead, which has a density about equal to that of water: a volume of 1.0 cm³ has a mass of about 1.0 g. Estimate the bead's acceleration in g's.

Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train's mass is 3.6 x 10⁵ kg, how much force must he exert? Compare to the weight of the train (give as %). How much force does the train exert on Superman?

An astronaut is inside a $2.25 × 10^6$ kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound ($331$ m/s) as quickly as possible, but astronauts are in danger of blacking out at an acceleration greater than $4g$. What force, in terms of the astronaut's weight $w$, does the rocket exert on her? Start with a free-body diagram of the astronaut.

(II) A high-speed 14-car Italian train has a mass of 640 metric tons (640,000 kg). It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum constant velocity (300 km/h), it exerts a force of about 150 kN. Calculate a) its maximum acceleration, and (b) estimate the total force of friction and air resistance at top speed.

A hockey puck with mass $0.160$ kg is at rest at the origin ($x=0$) on the horizontal, frictionless surface of the rink. At time $t=0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$-axis; she continues to apply this force until $t=2.00$ s. What are the position and speed of the puck at $t=2.00$ s?