Concept explainers
(a)
Speed of the projectile.
(a)
Answer to Problem 25P
The speed is
Explanation of Solution
Write the equation for
Here
Expand (I)
Here
Initial velocity is zero, then
Final extension is zero, then
Write the equation for final kinetic energy
Here,
Write the equation for initial potential energy.
Here
Substitute these results in (II) and arrange in terms of
Conclusion:
Substitute
The speed is
(b)
The point at which the ball has maximum speed.
(b)
Answer to Problem 25P
The maximum speed is achieved at
Explanation of Solution
Write the expression for force on a spring.
Here
Rewrite (VI) in terms of
.Conclusion:
Substitute
Therefore the ball must have moved,
The maximum speed is achieved at
(c)
Maximum speed of the projectile.
(c)
Answer to Problem 25P
The speed is
Explanation of Solution
Write the equation for final potential energy
Here
Substitute (III), (V), (VI0, and (X) in (II)
Rearrange (XI) in terms of
Conclusion:
Substitute
The speed is
Want to see more full solutions like this?
Chapter 7 Solutions
Principles of Physics: A Calculus-Based Text
- An intrepid physics student decides to try bungee jumping. She obtains a cord that is 9.00 m long and has a spring constant of 5.00 102 N/m. When fully suited, she has a mass of 70.0 kg. She looks for a bridge to which she can tie the cord and step off. Determine the minimum height of the bridge that will allow her to stay dry (that is, so that she stops just before hitting the water below). Assume air resistance is negligible.arrow_forwardA shopper weighs 3.00 kg of apples on a supermarket scale whose spring obeys Hookes law and notes that the spring stretches a distance of 3.00 cm. a. What will the springs extension be if 5.00 kg of oranges are weighed instead? b. What is the total amount of work that the shopper must do to stretch this spring a total distance of 7.00 cm beyond its relaxed position?arrow_forwardA helicopter rescues a trapped person of mass m = 65.0 kg from a flooded river by lifting the person vertically upward using a winch and rope. The person is pulled 12.0 m into the helicopter with a constant force that is 15% greater than the persons weight. a. Find the work done by each of the forces acting on the person. b. Assuming the survivor starts from rest, determine his speed upon reaching the helicopter.arrow_forward
- At the start of a basketball game, a referee tosses a basketball straight into the air by giving it some initial speed. After being given that speed, the ball reaches a maximum height ymax above where it started. Using conservation of energy, find expressions for a. the balls initial speed in terms of the gravitational acceleration g and the maximum height ymax and b. the height of the ball when it has speed v in terms of its current height y, the gravitational acceleration g, and the maximum height ymax.arrow_forwardA light spring is attached to a block of mass 4m at rest on a frictionless, horizontal table. A second block of mass m is now placed on the table, in contact with the free end of the spring, and the two blocks are pushed together (Fig. P10.78). When the blocks are released, the more massive block moves to the left at 2.50 m/s. a. What is the speed of the less massive block? b. If m = 1.00 kg, what is the elastic potential energy of the system before it is released from rest? FIGURE P10.78arrow_forwardOn a movie set, an alien spacecraft is to be lifted to a height of 30.0 m for use in a scene. The 200.0-kg spacecraft is attached by ropes to a massless pulley on a crane, and four members of the films construction crew lift the prop at constant speed by delivering 185 W of power each. If 20.0% of the mechanical energy delivered to the pulley is lost to friction, what is the time interval required to lift the spacecraft to the specified height?arrow_forward
- In three cases, a force acts on a particle, and the particle is displaced from an initial position to a final position. Figure 9.11 (page 255) shows the position-versus-force graphs, indicating the initial and final positions of the particle in each case. Find the work done by the force on the particle and sketch the force and displacement vectors along with the appropriate axis in each case.arrow_forwardA constant force of magnitude 4.75 N is exerted on an object. The forces direction is 60.0 counterclockwise from the positive x axis in the xy plane, and the objects displacement is r=(4.22.1j+1.6k)m. Calculate the work done by this force.arrow_forward(a) How long will it take an 850-kg car with a useful power output of 40.0 hp (1 hp equals 746 W) to reach a speed of 15.0 m/s, neglecting friction? (b) How long will this acceleration take if the car also climbs a 3.00-m high hill in the process?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University