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 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.

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 ?