Chapter 4: Linear Kinetics, Force and Newton’s Laws of Motion
Chapter 4: Linear Kinetics, Force and Newton’s Laws of Motion
Problems and Exercises
- *Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 30.0°. David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N.
(a) Find the magnitude of the resultant (net) force on the tree and the angle it makes with David’s rope.
- *While sliding a couch across a floor, Andrea and Jennifer exert forces on the couch. Andrea’s force is due north with a magnitude of 130.0 N and Jennifer’s force is 32° east of north with a magnitude of 180.0 N.
(a) Find the magnitude and direction of the net force. - *A 30.0-kg girl in a swing is pushed to one side and held at rest by a horizontal force 𝐅⃗ so that the swing ropes are 30.0° with respect to the vertical.
(a) Calculate the tension in each of the two ropes supporting the swing under these conditions.
(b) Calculate the magnitude of 𝐅⃗ - *Two muscles in the back of the leg pull upward on the Achilles tendon, as shown below. (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?
- *After a mishap, a 76.0-kg circus performer clings to a trapeze, which is being pulled to the side by another circus artist, as shown here. Calculate the tension in the two ropes if the person is momentarily motionless. Include a free-body diagram in your solution.
- *Andrea, a 63.0-kg sprinter, starts a race with an acceleration of 4.200 m/s2. What is the net external force on her?
- *If the sprinter from the previous problem accelerates at that rate for 20.00 m and then maintains that velocity for the remainder of a 100.00-m dash, what will her time be for the race?
- *Astronauts in orbit are apparently weightless. This means that a clever method of measuring the mass of astronauts is needed to monitor their mass gains or losses, and adjust their diet. 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 an astronaut’s acceleration is measured to be 0.893m/s2.
(a) Calculate her mass.
(b) By exerting a force on the astronaut, the vehicle in which she orbits experiences an equal and opposite force. Use this knowledge to find an equation for the acceleration of the system (astronaut and spaceship) that would be measured by a nearby observer.
(c) Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method by which recoil of the vehicle is avoided. - *Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second exerts a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg.
(a) What is the system of interest if the acceleration of the child in the wagon is to be calculated?
(