Chapter 1: Mechanics

Vectors$\overrightarrow{A}$and$\overrightarrow{B}$have scalar product$-6.00$, and their vector product has magnitude$+9.00$. What is the angle between these two vectors?

SHM of a Butcher’s Scale. A spring of negligible mass and force constant \(k = 400\;{\rm{N/m}}\) is hung vertically, and a 0.200-kg pan is suspended from its lower end. A butcher drops a 2.2-kg steak onto the pan from a height of 0.40 m. The steak makes a totally inelastic collision with the pan and sets the system into vertical SHM. What are (a) the speed of the pan and steak immediately after the collision; (b) the amplitude of the subsequent motion; (c) the period of that motion?

79.A uniform rod of length L rests on a frictionless horizontal surface. The rod pivots about a fixed frictionless axis at one end. The rod is initially at rest. A bullet traveling parallel to the horizontal surface and perpendicular to the rod with speed v strikes the rod at its center and becomes embedded in it. The mass of the bullet is one-fourth the mass of the rod. (a) What is the final angular speed of the rod? (b) What is the ratio of the kinetic energy of the system after the collision to the kinetic energy of the bullet before the collision?

A rifle bullet with mass 8.00 g strikes and embeds itself in a block with a mass 0.992 kg that rests on a frictionless, horizontal surface and is attached to a coil spring (Fig. P8.79). The impact compresses the spring 15.0 cm. Calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.250 cm. (a) Find the magnitude of the block’s velocity just after impact. (b) What was the initial speed of the bullet?

The work done by a force is the product of force and distance. The torque due to a force is the product of force and distance. Does this mean that torque and work are equivalent? Explain.

7. You can probably stand flatfooted on the floor and then rise up and balance on your tiptoes. Why are you unable to do it if your toes are touching the wall of your room? (Try it!)

Sketch the six graphs of the x- and y-components of position, velocity, and acceleration versus time for projectile motion with ${\mathit{x}}_{\mathbf{0}}\mathbf{=}{\mathit{y}}_{\mathbf{0}}\mathbf{=}\mathbf{0}\mathbf{}$and $\mathbf{0}\mathbf{<}{\mathit{\alpha }}_{\mathbf{0}}\mathbf{<}\mathbf{90}\mathbf{°}$.

When a car stops suddenly, the passengers tend to move forward relative to their seats. Why? When a car makes a sharp turn, the passengers tend to slide to one side of the car. Why?

In the conical pendulum of Example 5.20 (Section 5.4), which of the forces do work on the bob while it is swinging?

What is the purpose of the spin cycle of a washing machine? Explain in terms of acceleration components