A cog system on the beginning segment of a roller coaster needs to get 25 occupied cars up a 100-m vertical rise over a time interval of 60 s. Each car experiences a gravitational force of 5670 N. The cars start at rest and end up moving at 0.50 m/s. (a) How much work is done by the cog system on the cars? (b) What average power must the cog system supply? (c) What would happen to the amount of work done by the cog system if the cars had to be lifted the same distance in 30 s?

In pushing a 0.024-kg dart into a toy dart gun, you have to exert an increasing force that tops out at 6.0 N when the spring is compressed to a maximum value of 0.12 m. (a) What is the launch speed of the dart when fired horizontally? (b) Does your answer change if the dart is fired vertically?

In a carnival game, the player throws a ball at a haystack. For a typical throw, the ball leaves the hay with a speed exactly one-half of the entry speed. (a) If the frictional force exerted by the hay is a constant 6.0 N and the haystack is 1.2 m thick, derive an expression for the typical entry speed as a function of the inertia of the ball. Assume horizontal motion only, and ignore any effects due to gravity. (b) What is the typical entry speed if the ball has an inertia of a 0.50 kg?

Two 0.50-kg carts are pushed toward each other from starting positions at either end of a 6.0-m low-friction track. Each cart is pushed with a force of 3.0 N, and that force is exerted for a distance of 1.0 m. (a) What is the work done on the two-cart system? (b) What is the change in kinetic energy of the system? (c) What is the kinetic energy of the center of mass of the system?

Distinguish between the three different types of yeast doughs.

A 6.0-kg bowling ball is held 10 mm above a mattress and then released from rest and allowed to fall, sinking into the mattress. Model the mattress as a single spring with spring constant k = 500 N/m. (a) Calculate the ball’s kinetic energy, the gravitational potential energy of the system (ball, spring, and Earth), and the elastic potential energy at the following compression's: 0, 0.050 m, 0.10 m, 0.15 m, 0.20 m. (b) What is the maximum compression of the mattress? Ignore the inertia of the spring.

How might diamonds purchased in Europe fuel political and social instability in West Africa?

A number can have more than one factor tree. Can it have more than one prime factorization? Explain.

A beetle that has an inertia of $4.0 \times 10 ^ { - 6 } \mathrm { kg }$ sits on the floor. It jumps by using its muscles to push against the floor and raise its center of mass. (a) If its center of mass rises 0.75 mm while it is pushing against the floor and then continues to travel up to a height of 300 mm above the floor, what is the magnitude of the force exerted by the floor on the beetle? (b) What is the beetle’s acceleration during the motion?

A 1000-kg car traveling at 5.0 m/s runs into the side of an underpass. The concrete wall is not affected, but the car crumples such that in the time interval from the instant of impact to the instant at which the car comes to rest, its center of mass travels forward 0.50 m. What are (a) the magnitude of the average force exerted on the car, (b) the work done by the wall on the car, and (c) the change in kinetic energy of the car’s center of mass?

Choose the best answers to complete the sentences or to answer the following questions. The discovery of oil has attracted large numbers of migrants to the Arabian Peninsula from _________ A. the United States B. Europe C. South Asia D. East Asia

Two children pull a third child on a tricycle by means of two ropes tied to the handlebars. The combined inertia of the child and tricycle is 35 kg. One child pulls with a constant force of 100 N directed to the right of the straight-ahead direction at an angle of $45 ^ { \circ }$. (a) If the second child pulls with a force of 80 N, at what angle to the left of the straight-ahead direction must he pull to make the tricycle move straight ahead? (b) With the second child pulling at the angle you calculated in part a, what is the acceleration of the tricycle? (c) What is the work done on the tricycle by the two ropes if the children pull constantly like this while the tricycle moves 2.0 m?

What is the predominant type of natural vegetation found in Central America?

Find the indicated term of each arithmetic sequence.

$$a _ { 1 } = 10 , d = - 5 , n = 9$$