A 31.0-kg child on a 3.00-m-long swing is released from rest when the ropes of the swing make an angle of 29.0° with the vertical.(a) Neglecting friction, find the child's speed at the lowest position.m/s(b) If the actual speed of the child at the lowest position is 2.40 m/s, what is the mechanical energy lost due to friction?]

(a) Finding the child's speed at the lowest position (neglecting friction)Step 1: Understanding the…

Answered: A 31.0-kg child on a 3.00-m-long swing…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter7: Conservation Of Energy

Section: Chapter Questions

Problem 81P: Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with...

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A 5.00-kg block is set into motion up an inclined plane with an initial speed of i = 8.00 m/s (Fig. P7.21). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of = 30.0 to the horizontal. For this motion, determine (a) the change in the blocks kinetic energy, (b) the change in the potential energy of the block-Earth system, and (c) the friction force exerted on the block (assumed to be constant), (d) What is the coefficient of kinetic friction? Figure P7.21
An electric scooter has a battery capable of supplying 120 Wh of energy. If friction forces and other losses account for 60.0% of the energy usage, what altitude change can a rider achieve when driving in hilly ter-rain if the rider and scooter have a combined weight of 890 N?
A certain automobile engine delivers 2.24 104 W (30.0 hp) to its wheels when moving at a constant speed of 27.0 m/s ( 60 mi/h). What is the resistive force acting on the automobile at that speed?
A force F = (6i 2j) N acts on a panicle that under-goes a displacement r = (3i + j) m. Find (a) the work done by the force on the particle and (b) the angle between F and r.
A 500-kg dragster accelerates from rest to a final speed of 110 m/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts and horsepower if this takes 7.30s?
A cat plays with a toy mouse suspended from a light string of length 1.25 m, rapidly batting the mouse so that it acquires a speed of 2.75 m/s while the string is still vertical. Use energy conservation to find the mouses maximum height above its original position. (Assume the string always remains taut.)
A 1.50 103-kg car starts from rest and accelerates uniformly to 18.0 m/s in 12.0 s. Assume that, air resistance remains constant at 4.00 102 N during this time. Find (a) the average power developed by the engine and (b) the instantaneous power output of the engine at t = 12.0 s, just before the car stops accelerating.
A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P7.79). The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point , the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The blocks speed at the bottom of the track is = 12.0 m/s, and the block experiences an average friction force of 7.00 N while sliding up the track. (a) What is x? (b) If the block were to reach the top of the track, what would be its speed at that point? (c) Does the block actually reach the top of the track, or does it fall off before reaching the top?
Give an example of a situation in which there is a force and a displacement, but the force does no work. Explain why it does no work.
A particle of mass 2.0 kg moves under the influence of the force F(x)=(5x2=7x)N . Suppose a frictional force also acts on the particle. If the particle’s speed when it starts at x=4.0 m is 0.0 m/s and when it arrives at x=4.0 m is 9.0 m/s, how much work is done on it by the frictional force between x=4.0 m and x=4.0 m?
As a mass tied to the end of a string strings from its highest point down to its lowest point, it is acted on by three forces: gravity, tension, and air resistance. Which force does (a) positive work? (b) negative work? (c) zero work?
Consider a block of mass 0.200 kg attached to a spring of spring constant 100 N/m. The block is placed on a frictionless table, and the other end of the spring is attached to the wall so that the spring is level with the table. The block is then pushed in so that the spring is compressed by 10.0 cm. Find the speed of the block as it crosses (a) the point when the spring is not stretched, (b) 5.00 cm to the left of point in (a), and (c) 5.00 cm to the right of point in (a).

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