Work-Energy

A cord is used to vertically lower an initially stationary block of mass M at a constant downward acceleration of g/4. When the block has fallen a distance d, find

In Figure, a block of mass $m$ lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (spring constant $k$) whose other end is fixed. The block is initially at rest at the position where the spring is unstretched ($x=0$) when a constant horizontal force $\vec{F}$ in the positive direction of the $x$ axis is applied to it. A plot of the resulting kinetic energy of the block versus its position $x$ is shown in Fig. 7-36. The scale of the figure's vertical axis is set by $K_s = 4.0$ J.

A 2.00 kg particle is moved from rest along an x axis by an applied force. The figure shows the particle's acceleration $a$ versus its position $x$ from $x=0$ to $x=9.0$ m. The vertical axis scale is set by $a_s = 6.0$ m/s$^2$.

A 2.0 kg lunchbox is sent sliding over a frictionless surface in the positive direction of an x axis. Beginning at time $t = 0$, a steady wind pushes on the lunchbox in the negative direction of the x axis. The figure shows the position $x$ of the lunchbox as a function of time $t$.

As a particle moves along an x axis, a force in the positive direction of the axis acts on it. The provided figure shows the magnitude $F$ of the force versus position $x$ of the particle. The curve is given by $F = a/x^2$, with $a = 9.0 \text{ N} \cdot \text{m}^2$.

When a click beetle is upside down on its back, it jumps upward by suddenly arching its back. Videotape of a certain click-beetle jump shows that a beetle of mass $m = 4.0 \times 10^{-6}$ kg moved directly upward by $d = 0.77$ mm during the launch and then to a maximum height of $h = 0.30$ m.

From the edge of a cliff, a 0.55 kg projectile is launched with an initial kinetic energy of 1550 J. The projectile's maximum upward displacement from the launch point is +140 m.