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.

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in given figure. (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by this force?

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.

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.

(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 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?

Explain why the neutralization reaction of a strong acid and a weak base gives a weakly acidic solution.

Suppose Kevin, a 60.0-kg gymnast, climbs a rope. (a) What is the tension in the rope if he climbs at a constant speed? (b) What is the tension in the rope if he accelerates upward at a rate of 1.50 m/s²?

A real process may be nearly adiabatic if it occurs over a very short time. How does the short time span help the process to be adiabatic?

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?

A truck collides with a car, and during the collision, the net force on each vehicle is essentially the force exerted by the other. Suppose the mass of the car is $550 \mathrm{~kg}$, the mass of the truck is $2200 \mathrm{~kg}$, and the magnitude of the truck's acceleration is $10 \mathrm{~m} / \mathrm{s}^2$. Find the magnitude of the car's acceleration.

A ball is thrown horizontally from the top of a 60.0-m building and lands 100.0 m from the base of the building. Ignore air resistance. (a) How long is the ball in the air? (b) What must have been the initial horizontal component of the velocity? (c) What is the vertical component of the velocity just before the ball hits the ground? (d) What is the velocity (including both the horizontal and vertical components) of the ball just before it hits the ground?

Andrea, a $63.0-\mathrm{kg}$ sprinter, starts a race with an acceleration of $4.200 \mathrm{~m} / \mathrm{s}^2$. What is the net external force on her?

Write the chemical formula and Lewis structure of the following, each of which contains five carbon atoms: (a) an alkane (b) an alkene (c) an alkyne