9. Work & Energy

A particle with mass m and velocity v has kinetic energy K. What is the kinetic energy of a particle with mass m/2 and velocity 2v?

Block A has mass $20\mathrm{kg}$ and block B has mass $50\mathrm{kg}$. Starting from rest, the two blocks are pushed by identical forces through a distance of $10\mathrm{m}$. Which block (if either) is going faster at end of the $10\mathrm{m}$? Which block (if either) has the greatest kinetic energy at the end of the $10\mathrm{m}$?

What is the kinetic energy of a $500\mathrm{kg}$ car traveling at $27\mathrm{m}/\mathrm{s}$ (about $60\mathrm{mph}$)?

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

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?

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 45 g bug is hovering in the air. A gust of wind exerts a force F (→ above F) = (4.0î-6.0ĵ) x 10¯² N on the bug. (b) What is the bug's speed at the end of this displacement? Assume that the speed is due entirely to the wind.

How much work does tension do to pull the mass from the bottom of the hill (θ = 0) to the top at constant speed? To answer this question, write an expression for the work done when the mass moves through a very small distance ds while it has angle θ, replace ds with an equivalent expression involving R and dθ , then integrate.

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. (c) How long does it take the Porsche to reach the maximum power output?

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. (b) If the Porsche accelerates at aₘₐₓ, what is its speed when it reaches maximum power output?

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. (a) What is the maximum acceleration of the Porsche on a concrete surface where μₛ = 1.00 ? Hint: What force pushes the car forward?

A 150 g particle at x = 0 is moving at 2.00 m/s in the + x - direction. As it moves, it experiences a force given by Fₓ = (0.250 N) sin (x/2.00 m) . What is the particle's speed when it reaches x = 3.14 m ?

T ─ (1500 kg) (9.8 m/s²) = (1500 kg) (1.0 m/s²) P = T (2.0 m/s) (a) Write a realistic problem for which this is the correct equation(s).

A particle moving on the x-axis experiences a force given by Fx = qx², where q is a constant. How much work is done on the particle as it moves from x=0 to x=d?

T ─ (1500 kg) (9.8 m/s²) = (1500 kg) (1.0 m/s²) P = T (2.0 m/s) (b) Draw a pictorial representation.

T ─ (1500 kg) (9.8 m/s²) = (1500 kg) (1.0 m/s²) P = T (2.0 m/s) (c) Finish the solution of the problem.

The gravitational attraction between two objects with masses mᴀ and mᴃ, separated by distance 𝓍, is F = Gmᴀmᴃ/𝓍², where G is the gravitational constant. (b) 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 ..

CALC An object moving in the xy-plane is subjected to the force F(arrow on top) =(2xy î+x² ĵ) N, where x and y are in m. c. Is this a conservative force?

CALC An object moving in the xy-plane is subjected to the force F(arrow on top) =(2xy î+x² ĵ) N, where x and y are in m. a. 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?