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Chapter 4: Q1PE (page 161)

A 63.0 kg sprinter starts a race with an acceleration of 4.20 m/s2. What is the net external force on him?

Short Answer

Expert verified

The net external force is 264.6 N.

Step by step solution

01

Given Data

The given data is listed as below,

  • Mass of the sprinter is, m= 63 kg.

  • Acceleration is, a= 4.20 m/s2.

02

Concept of Newton’s second law of motion

Significant Newton’s second law of motion states that the acceleration of a system is directly proportional to the net external force acting on the system and is inversely proportional to the mass of the system. Mathematically,

Fnet=ma ………. (i)

Here,

(a).Fnetis the net force

(b). mis the mass

(c).a is the acceleration.

03

Determine the net external force acting on the sprinter

Substitute 63 kg for mand 4.20 m/s2 for a in equation (i),

Fnet=63kg×4.20m/s2=264.6kg‐m/s2=264.6N

Hence, the net external force on him is 264.6 N.

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Most popular questions from this chapter

Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be 0.893 m/s2.

(a) Calculate her mass.

(b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which recoil of the vehicle is avoided.

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?

In a traction setup for a broken bone, with pulleys and rope available, how might we be able to increase the force along the femur using the same weight? (See Figure 4.30.) (Note that the femur is the shin bone shown in this image.

(a) Find the magnitudes of the forces F1 and F2 that add to give the total force Ftot shown in Figure 4.35. This may be done either graphically or by using trigonometry.

(b) Show graphically that the same total force is obtained independent of the order of addition of F1and F2 .

(c) Find the direction and magnitude of some other pair of vectors that add to give Ftot . Draw these to scale on the same drawing used in part (b) or a similar picture.

Figure 4.39 shows Superhero and Trusty Sidekick hanging motionless from a rope. Superhero’s mass is 90.0 kg, while Trusty Sidekick’s is 55.0 kg, and the mass of the rope is negligible.

(a) Draw a free-body diagram of the situation showing all forces acting on Superhero, Trusty Sidekick, and the rope.

(b) Find the tension in the rope above Superhero.

(c) Find the tension in the rope between Superhero and Trusty Sidekick. Indicate on your free-body diagram the system of interest used to solve each part.
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