Exam 7: Work and Energy

When you drop a pebble from height H,it reaches the ground with speed V assuming there is no air resistance.From what height should you drop it so it will reach the ground with twice speed?

At what minimum rate is a 60.0-kg boy converting his internal energy when,in 8.00 s,he runs up a flight of stairs that is 10.0-m high?

If you want to double the momentum of a gas molecule,by what factor must you increase its kinetic energy?

Planet W-70 has a radius of 2.48 × 10⁷ m and an escape velocity of 23,300 m/s.What is the mass of W-70? (G = 6.67 × 10^-11 N ∙ m²/kg²)

What is the minimum energy needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s?

A block of mass m = 3.6 kg,moving on a frictionless surface with a speed $\mathrm { v } _ { \mathrm { i } } = 9.3 \mathrm {~m} / \mathrm { s }$ makes a sudden perfectly elastic collision with a stationary block of mass M,as shown in the figure.Just after the collision,the 3.6-kg block recoils with a speed of $v _ { \mathrm { f } } = 2.7 \mathrm {~m} / \mathrm { s }$ What is the speed V of the other block?

A heavy sled and a light sled,both moving horizontally with the same speed,suddenly slide onto a rough patch of snow and eventually come to a stop.The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them.Which of the following statements about these sleds are correct? (There could be more than one correct choice.)

A stone (the system)with a mass of 1.0 kg is tied to the end of a light string which keeps it moving in a circle with a constant speed of 4.0 m/s on a perfectly smooth horizontal tabletop.The radius of the path is 0.60 m.How much work does the force exerted by the string do on the stone as it makes one-half of a complete circle?

In the past,Earth has been hit by many asteroids,some very large.Suppose one such asteroid approached Earth so that when it was very far away it was traveling at 6500 m/s along a line that would miss the center of Earth by 8,500,000 m.Because of the gravitational attraction of Earth,it departed from this straight line and curved towards Earth,colliding with it.What was the speed of this asteroid when it hit Earth if we ignore the effect of the sun? The mass of Earth is 5.97 × 10²⁴ kg,its radius is 6.38 × 10⁶ m,and G = 6.67 × 10^-11 N ∙ m²/kg².

On a frictionless horizontal surface,a 1.50-kg mass traveling at 3.50 m/s suddenly collides with and sticks to a 3.00-kg mass that is initially at rest,as shown in the figure.This system then runs into an ideal spring of force constant (spring constant)50.0 N/cm. (a)What will be the maximum compression distance of the spring? (b)How much mechanical energy is lost during this process? During which parts of the process (the collision and compression of the spring)is this energy lost?

How high a hill would a 75-kg hiker have to climb to increase her gravitational potential energy by 10,000 J?