Consider a runner in lane 1 with a speed v1v1 and a runner in lane 4 with a speed v4, where the ratio of the speeds v4/v1 is 2. The radius of lane 4 is b times the radius of lane 1, and both runners have the same mass. Which of the following claims is correct about the net forces F1F1 and F4 exerted on the runners in lanes 1 and 4, respectively?
F4 is equal to 4/b F1.
Key Terms
Consider a runner in lane 1 with a speed v1v1 and a runner in lane 4 with a speed v4, where the ratio of the speeds v4/v1 is 2. The radius of lane 4 is b times the radius of lane 1, and both runners have the same mass. Which of the following claims is correct about the net forces F1F1 and F4 exerted on the runners in lanes 1 and 4, respectively?
F4 is equal to 4/b F1.
Consider a runner in any of the lanes moving at a known, constant tangential speed. Which of the following measuring tools, if any, could be used to experimentally determine the centripetal acceleration of the runner?
Meterstick
Now consider four runners running around the track with the same constant tangential speed, with one runner in each lane of the track. A student is considering using the following equations to determine which runner has the greatest acceleration.
Equation 1: v2x=v2x0+2ax(x−x0)vx2=vx02+2ax(x−x0)
Equation 2: ac=v2rac=v2r
Which equation should the student use, and why?
Equation 2, because the radius of the circular path traveled by a runner determines the acceleration of the runner.
A truck in a traffic circle travels in a circular path at constant speed v0v0 while passing through region XX of the circle, as shown in Figure 1 above. A diagram representing the forces exerted on the truck in region XX is shown in Figure 2. At a later time a car with less mass than the truck passes through region XX at the same speed and the same distance from the center of the traffic circle as the truck. The coefficient of friction between the car's tires and the ground is the same as that for the truck's tires and the ground. Which of the following diagrams could represent the forces exerted on the car in region XX compared to the truck in region XX ? Assume that the length of each arrow is proportional to the magnitude of the force represented by the arrow.
^ normal||<-O friction||^ gravity
A student swings a ball of mass MM on the end of a string in a vertical circle of radius R, as shown in the top figure above. Also shown is a diagram representing all of the forces exerted on the ball at the bottom of the circle, where its speed is v0v0. What is the magnitude of the acceleration of the ball at the bottom of the circle?
Ftentsion -Fgravity/M
The figure above shows two identical asteroids that are located near each other but are not in contact. Various locations are also labeled on the asteroids. If an astronaut wants to stand on one of the asteroids and experience the largest net gravitational force, where should the astronaut stand?
Location A
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| Term | Definition |
|---|---|
Consider a runner in lane 1 with a speed v1v1 and a runner in lane 4 with a speed v4, where the ratio of the speeds v4/v1 is 2. The radius of lane 4 is b times the radius of lane 1, and both runners have the same mass. Which of the following claims is correct about the net forces F1F1 and F4 exerted on the runners in lanes 1 and 4, respectively? | F4 is equal to 4/b F1. |
Consider a runner in any of the lanes moving at a known, constant tangential speed. Which of the following measuring tools, if any, could be used to experimentally determine the centripetal acceleration of the runner? | Meterstick |
Now consider four runners running around the track with the same constant tangential speed, with one runner in each lane of the track. A student is considering using the following equations to determine which runner has the greatest acceleration. | Equation 2, because the radius of the circular path traveled by a runner determines the acceleration of the runner. |
A truck in a traffic circle travels in a circular path at constant speed v0v0 while passing through region XX of the circle, as shown in Figure 1 above. A diagram representing the forces exerted on the truck in region XX is shown in Figure 2. At a later time a car with less mass than the truck passes through region XX at the same speed and the same distance from the center of the traffic circle as the truck. The coefficient of friction between the car's tires and the ground is the same as that for the truck's tires and the ground. Which of the following diagrams could represent the forces exerted on the car in region XX compared to the truck in region XX ? Assume that the length of each arrow is proportional to the magnitude of the force represented by the arrow. | ^ normal||<-O friction||^ gravity |
A student swings a ball of mass MM on the end of a string in a vertical circle of radius R, as shown in the top figure above. Also shown is a diagram representing all of the forces exerted on the ball at the bottom of the circle, where its speed is v0v0. What is the magnitude of the acceleration of the ball at the bottom of the circle? | Ftentsion -Fgravity/M |
The figure above shows two identical asteroids that are located near each other but are not in contact. Various locations are also labeled on the asteroids. If an astronaut wants to stand on one of the asteroids and experience the largest net gravitational force, where should the astronaut stand? | Location A |
A student conducts three experiments to determine how certain quantities influence the centripetal force responsible for an object to spin in a horizontal circle. The student uses one end of a string to attach the object while the other end is connected to a force sensor that allows the student to change the tension on the string, as shown in the figure. The student records data from the three experiments in the table above. Which of the following experiments, if any, collected data that do not agree with the expression for the net centripetal force on the object? | All the data are expected. |
At one point in their individual orbits, three planets, X,Y,& Zare along the same horizontal line. The gravitational force on Planet X from Planet Z is F0. The distance from the center of mass of each planet to an adjacent planet is given in terms of R0, and their respective masses are given in terms of M0, as shown above. What is the net force on Planet Y, and what reasoning supports this claim? | 5F0 to the right, because the gravitational force from Planet Y is greater than the gravitational force from Planet X. |
A planet orbits a star in the path shown in the figure. The planet's mass is much smaller than the star's mass. Which two of the following claims are correct about the accelerations associated with the planet, star, and planet-star system? Select two answers. Justify your selections. | -Both the planet and the star accelerate, because each object exerts a force on the other object. -The center of mass of the planet-star system does not accelerate, because there is no net force exerted on the system. |
A satellite moves in a circular orbit at a constant speed v0 around Earth at a distance R from its center. The force exerted on the satellite is F0. An identical satellite orbits Earth at a distance of 3R from the center of the Earth. How does the tangential speed, vT, of the satellite at distance 3R compare to the speed v0 of the satellite at R? | vT= 1 / √3 x v0 |
A car travels with a tangential speed v1 around a curve of radius r and turns to the left, as shown by the rear view of the car in Figure 1. A force diagram of the forces exerted on the car with speed of 5m/s as it turns is shown in Figure 2. A force diagram of the forces exerted on the car with speed v as it turns around the same curve of the same radius is shown in Figure 3. The speed v of the car in figure 3 is most nearly | The speed v of the car in figure 3 is most nearly 15 m/s. |