Intro to Energy & Kinetic Energy Practice Problems

A proton of mass 1.6726 × 10^-27 kg and a deuteron of mass 3.34364 × 10^-27 kg have the same amount of kinetic energy. Find the speed of the proton (v_p) in terms of the speed of the deuteron (v_d).

A 350 kg motorcycle travels at a speed of 12 m/s. Find the speed that a 60 kg downhill skier should reach in order to produce the same amount of kinetic energy as the motorbike.

Is it realistic to assume that a sprinter of mass 70 kg could run fast to have a kinetic energy of 2600 J?

A car's engine has a variable power output. The net force on the car follows the relation F_y = ky⁴, where k is a proportionality constant. Determine the work done on the car when it covers a length y = 0 to y = L. 

For T - (2000 kg)(9.8 m/s²) = (2000 kg)(3.0 m/s²) and P = T(6.0 m/s), select the choice that describes a situation that matches the given equation.                                                                                                              

At x = 0 m, a ball moves with a speed of 3.5 m/s along the positive x-direction. During the motion, the ball encounters an external force, F(x) = (0.750 N)sin(0.2x m^-1). Determine the ball's speed at x = 5.21 m if it weighs 200 g.

Newton's law of universal gravitation gives the gravitational force of attraction between two objects with mass as F = Gm₁m₂/r², where G is the universal gravitation constant (G = 6.67 × 10^-11 N•m²/kg²),  m₁ and m₂ are the masses of the objects and r is their separation. Using Newton's second law, if one object is more massive, the massive object remains at rest while the lighter object moves towards it. If a space boulder with a mass of 1.20 × 10⁹ kg passes Jupiter's orbit directly toward the sun at a speed of 54.0 km/s, determine the speed of the boulder when it reaches the Earth's orbit. Use any necessary astronomical data from literature sources.

A loaded heavy construction vehicle has a mass of 9850 kg. The power output of the engine is 420 hp. The engine and transmission dissipate 15% of the power output, delivering 85 % to the wheels. Suppose 80% of the vehicle's weight is carried by the drive wheels; determine the greatest acceleration of the vehicle on a tarmac road when μ_s = 1.2.

A pick-up truck's engine delivers a maximum power of 120 hp. The truck is loaded to a total mass of 2250 kg. Inefficiencies in the engine and transmission dissipate 20% of the generated power while 80% is successfully delivered to the drive wheels. The truck's mass is distributed, so the drive wheels carry 3/5 of the total mass. When the truck accelerates at maximum acceleration (µ_s = 0.90), determine the speed attained at maximum power output. Hint: draw a free-body diagram of the truck.

The engine of a passenger vehicle generates a maximum power of 200 hp. At one instance, it is loaded to a total mass of 4500 kg. Engine and transmission losses dissipate 25% of the power generated by the engine, while 75% is successfully transferred to the drive wheels. Using a mass distribution where the drive wheels bear 60% of the loaded vehicle mass, determine the time the vehicle takes to attain maximum power output. Assume the vehicle accelerates at a_max on a surface with a static friction coefficient, μₛ = 1.12.

A flat section of the earth's surface has a depression with straight/parabolic walls. Determine the work done by a force that pulls a mass from the lowest point in the depression where θ = 0 to a point out of the depression at a constant speed. Hint: Work out an expression for work done in moving the mass through a tiny distance dL when its orientation is θ. Substitute for dL with an appropriate expression with R and dθ before integrating.

A box is subjected to a 2D force, F = (xy² i + 3xyj) N, which depends on the x and y positions. The x and y coordinates are measured in m. The box starts at the origin and moves straight to (0,m). The box takes a right-angled turn and moves straight to (n,m). Determine the work done by the force.

A 58.0 g tennis ball is shot upward into the air. A breeze exerts a 2D horizontal force F = (3.0 i - 5.0j) × 10^-2 N on the ball. The ball makes a displacement of (1.5 i - j) m. Determine the magnitude of the ball's horizontal velocity after the displacement. Assume the vertical velocity has no effect on horizontal velocity and the breeze is the only source of the horizontal speed.

A boulder experiences 2D forces that vary with position according to F = [xy i + (1/2)x² j] N. The positions x, and y are in m. State (with reason) if the force is conservative.

What is the velocity of a nitrogen molecule at room temperature, given its kinetic energy is 5.41 x 10^-26 J and mass is 6.31 x 10^-21 kg?

A spacecraft of mass m_sp orbits the Earth in a circular path with a radius r_sp. Obtain an expression for the kinetic energy K_sp of the spacecraft.

Spacecrafts, P and Q, have been deployed to orbit around the center of the Earth. Spacecraft P is moving at an altitude of 5.50$\times$10³ km, while spacecraft Q is at an altitude of 10.8$\times$10³ km. Determine the kinetic energies of P and Q, if their mass is 2.00$\times$10³ kg each. Assume the orbits are circular.

Hint: gravitational constant G = 6.67$\times$10^-11 Nm²/kg², mass of earth M_E = 5.98$\times$10²⁴ kg, radius of earth = 6.38$\times$10⁶ m