9. Work & Energy

About 50,000 years ago, a meteor crashed into the earth near present-day Flagstaff, Arizona. Some estimates suggest this meteor had a mass of about 1.4×10⁸ kg and released 1×10¹⁶ J of energy when it slammed into the Earth. Calculate the approximate speed of this meteor before impact.

(II) For a satellite of mass m_S in a circular orbit of radius r_S around the Earth, determine its kinetic energy K.

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

At room temperature, an oxygen molecule, with mass of 5.31 x 10⁻²⁶ kg, typically has a kinetic energy of about 6.21 x 10⁻²¹ J . How fast is it moving?

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 $\vec{F}=(4.0\hat{ı}-6.0\hat{ȷ})\times {10}^{-2}\text{N}$ 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.

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. 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. If the Porsche accelerates at a_max, 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. What is the maximum acceleration of the Porsche on a concrete surface where μ_s = 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?