An astronaut is inside a $2.25\times {10}^6$ 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 is the maximum initial thrust this rocket's engines can have but just barely avoid blackout? Start with a free-body diagram of the rocket.

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.

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The $210$-kg capsule hit the ground at $311$ km/h and penetrated the soil to a depth of $81.0$ cm. What force did the ground exert on the capsule during the crash? Express the force in newtons and as a multiple of the capsule's weight.

Problems 35, 36, 37, 38, 39, and 40 show a free-body diagram. For each: Identify the direction of the acceleration vector a and show it as a vector next to your diagram. Or, if appropriate, write a = 0.

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if The force is halved and the object's mass is doubled?

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if the force is halved?

A single force with x-component Fₓ acts on a 2.0 kg object as it moves along the x-axis. A graph of Fₓ versus t is shown in FIGURE P5.32. Draw an acceleration graph aₓ versus t) for this object.

A single force with x-component Fₓ acts on a 500 g object as it moves along the x-axis. The object's acceleration graph aₓ versus t) is shown in FIGURE P5.30. Draw a graph of Fₓ versus t.