Dynamics: Force and Newton's Laws of Motion

Integrated Concepts When starting a foot race, a 70.0-kg sprinter exerts an average force of 650 N backward on the ground for 0.800 s.

(a) What is his final speed?

(b) How far does he travel?

A large rocket has a mass of 2.00×10⁶ kg at takeoff, and its engines produce a thrust of 3.50×10⁷ N.

(a) Find its initial acceleration if it takes off vertically.

(b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust?

(c) In reality, the mass of a rocket decreases significantly as its fuel is consumed. Describe qualitatively how this affects the acceleration and time for this motion.

A basketball player jumps straight up for a ball. To do this, he lowers his body 0.300 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.900 m above the floor.

(a) Calculate his velocity when he leaves the floor.

(b) Calculate his acceleration while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.300 m.

(c) Calculate the force he exerts on the floor to do this, given that his mass is 110 kg.

Integrated Concepts 

A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m. 

(a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar.

(b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as it goes from zero to the velocity found in (a). 

(c) What is the average force on the shell in the mortar? Express your answer in newtons and as a ratio to the weight of the shell.

Integrated Concepts 

An elevator filled with passengers has a mass of 1700 kg.

(a) The elevator accelerates upward from rest at a rate of 1.20 m/s² for 1.50 s. Calculate the tension in the cable supporting the elevator.

(b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time?

(c) The elevator decelerates at a rate of 0.600 m/s2 for 3.00 s. What is the tension in the cable during deceleration? 

(d) How high has the elevator moved above its original starting point, and what is its final velocity?

(a) What is the final velocity of a car originally traveling at 50.0 km/h that decelerates at a rate of 0.400 m/s² for 50.0 s? 

(b) What is unreasonable about the result?

(c) Which premise is unreasonable, or which premises are inconsistent?

Unreasonable Results

A 75.0-kg man stands on a bathroom scale in an elevator that accelerates from rest to 30.0 m/s in 2.00 s.

(a) Calculate the scale reading in newtons and compare it with his weight. (The scale exerts an upward force on him equal to its reading.)

(b) What is unreasonable about the result?

(c) Which premise is unreasonable, or which premises are inconsistent?

(a) What is the strength of the weak nuclear force relative to the strong nuclear force? 

(b) What is the strength of the weak nuclear force relative to the electromagnetic force? 

Since the weak nuclear force acts at only very short distances, such as inside nuclei, where the strong and electromagnetic forces also act, it might seem surprising that we have any knowledge of it at all. We have such knowledge because the weak nuclear force is responsible for beta decay, a type of nuclear decay not explained by other forces.

(a) What is the ratio of the strength of the gravitational force to that of the strong nuclear force? 

(b) What is the ratio of the strength of the gravitational force to that of the weak nuclear force? 

(c) What is the ratio of the strength of the gravitational force to that of the electromagnetic force? What do your answers imply about the influence of the gravitational force on atomic nuclei?

What is the ratio of the strength of the strong nuclear force to that of the electromagnetic force? Based on this ratio, you might expect that the strong force dominates the nucleus, which is true for small nuclei. Large nuclei, however, have sizes greater than the range of the strong nuclear force. At these sizes, the electromagnetic force begins to affect nuclear stability. These facts will be used to explain nuclear fusion and fission later in this text.