A freight train consists of two

$$8.00 × 10^5-kg$$

engines and 45 cars with average masses of

$$5.50 × 10^5 kg.$$

(a) What force must each engine exert backward on the track to accelerate the train at a rate of

$$5.00 × 10^{-2} m/s^2$$

if the force of friction is

$$7.50 × 10^5 N,$$

assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently, trains are very energy-efficient transportation systems. (b) What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?

Write the polynomial in standard form. Identify the leading coefficient.

$$- y ^ { 3 } + 3 y - 3 y ^ { 2 } + 2$$

A freight train consists of two $8.00 \times 10^{5}-\mathrm{kg}$ engines and 45 cars with average masses of $5.50 \times 10^{5}\ \mathrm{kg}.$ (a) What force must each engine exert backward on the track to accelerate the train at a rate of $5.00 \times 10^{-2}\ \mathrm{m} / \mathrm{s}^{2}$ if the force of friction is $7.50 \times 10^{5}\ \mathrm{N},$ assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (b) What is the magnitude of the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?

A freight train consists of two $8.00 \times 10^4-\mathrm{kg}$ engines and 45 cars with average masses of $5.50 \times 10^4 \mathrm{~kg}$. What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?

The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 250 N and the acceleration of the car is $1.80\ \mathrm{m} / \mathrm{s}^{2},$ what is the mass of the car plus its occupants? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton's laws of motion. For this situation, draw a free-body diagram and write the net force equation.

The table shows the number of hours you studied before your eight math tests and your percent score on each test.

A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has a capacitance of $8.00 \mu \mathrm { F }$, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to $6.00 \times 10 ^ { 2 } \mathrm { V }$?

To maintain a constant speed, the force provided by a car's engine must equal the drag force plus the force of friction of the road (the rolling resistance). (a) What are the drag forces at 70 km/h and 100 km/h for a Toyota Camry? (Drag area is 0.70 m²) (b) What is the drag force at 70 km/h and 100 km/h for a Hummer H2? (Drag area is 2.44 m²) Assume all values are accurate to three significant digits.

(a) What net external force is exerted on a 1100.0-kg artillery shell fired from a battleship if the shell is accelerated at

$$2.40 × 10^4 m/s^2?$$

(b) What is the magnitude of the force exerted on the ship by the artillery shell, and why?

A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate the magnitude of his cart's acceleration.

Calculate the maximum acceleration of a car that is heading down a 6.00° slope (one that makes an angle of 6.00° with the horizontal) under the following road conditions. You may assume that the weight of the car is evenly distributed on all four tires and that the coefficient of static friction is involved - that is, the tires are not allowed to slip during the deceleration. (Ignore rolling.) Calculate for a car: (a) On dry concrete. (b) On wet concrete. (c) On ice, assuming that

$$μ_s = 0.100,$$

the same as for shoes on ice.

A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate the magnitude of its acceleration.

What force does a trampoline have to apply to a 45.0-kg gymnast to accelerate her straight up at $7.50\ \mathrm{m} / \mathrm{s}^{2} ?$ Note that the answer is independent of the velocity of the gymnast-she can be moving either up or down, or be stationary.

Calculate the force a piano tuner applies to stretch a steel piano wire by 8.00 mm, if the wire is originally 1.35 m long and its diameter is 0.850 mm.