9. Work & Energy

How are $\mathrm{potential energy}$ and $\mathrm{kinetic energy}$ related in a closed system?

At what speed does a 1000 kg compact car have the same kinetic energy as a 20,000 kg truck going 25 km/h?

A cantilever behaves like an ideal spring with a spring constant of $k$. What is the mechanical work done by the cantilever when its extension increases from $10nm$ to $15nm$?

Which of the following is a form of kinetic energy?

The gravitational attraction between two objects with masses m_A and m_B, separated by distance 𝓍, is F = Gm_Am_B/𝓍², where G is the gravitational constant. If one mass is much greater than the other, the larger mass stays essentially at rest while the smaller mass moves toward it. Suppose a 1.5 x 10¹³ kg comet is passing the orbit of Mars, heading straight for the sun at a speed of 3.5 x 10⁴ m/s. What will its speed be when it crosses the orbit of Mercury? Astronomical data are given in the tables at the back of the book, and G = 6.67 x 10^-11 Nm²/kg².

Draw a pictorial representation.

$T-(1500\,\(\text{kg}\))(9.8\,\(\text{m/s}\)^2)=(1500\,\(\text{kg}\))\(\left\)(1.0\,\(\text{m/s}\)^2\(\right\))$

$P=T(2.0\,\(\text{m/s}\))$

A mother has four times the mass of her young son. Both are running with the same kinetic energy. What is the ratio v_son/v_mother of their speeds?

A 45 g bug is hovering in the air. A gust of wind exerts a force $\vec{F}=(4.0\hat{ı}-6.0\hat{ȷ})\times {10}^{-2}\text{N}$ on the bug. What is the bug's speed at the end of this displacement? Assume that the speed is due entirely to the wind.

CALC An object moving in the xy-plane is subjected to the force $\vec{F}=(2xy\hat{i}+x^2\hat{j})\text{N}$, where x and y are in m. The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis. How much work does the force do?

A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the engine and the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1480 kg, and two-thirds of the weight is over the drive wheels. What is the maximum acceleration of the Porsche on a concrete surface where μ_s = 1.00? Hint: What force pushes the car forward?

Is it reasonable that a $30$-kg child could run fast enough to have $100$ J of kinetic energy?