A toy car speeds up at 1.0 m/s2 while rolling down a ramp, and slows down at a rate of 2.0 m/s2 while rolling up the same ramp. What is the slope of the ramp in degrees? Grade in %? The friction coefficient?

A toy car speeds up at 1.0 m/s2 while rolling down a ramp, and slows down at a rate of 2.0 m/s2 while rolling up the same ramp. What is the slope of the ramp in degrees? Grade in %? The friction coefficient?

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Circular Motion And Other Applications Of Newton’s Laws

Section: Chapter Questions

Problem 6.22P: A child lying on her back experiences 55.0 N tension in the muscles on both sides of her neck when...

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The mass of a roller-coaster car, including its passengers, is 500 kg. Its speed at the bottom of the track in Figure P6.16 is 19 m/s. The radius of this section of the track is r1 = 25 m. Find the force that a seat in the roller-coaster car exerts on a 50-kg passenger at the lowest point.
A man whirls a 0.20-kg piece of lead attached to the end of a string of length 0.500 m in a circular path and in a vertical plane. If the man maintains a constant speed of 4.00 m/s, what is the tension in the string when the lead is (a) at the top of the circular path? (b) at the bottom of the circular path? (Sec Section 7.4.)
In Figure P3.55, a spider is resting after starting to spin its web. The gravitational force on the spider makes it exert a downward force of 0.150 N on the junction of the three strands of silk. The junction is supported by different tension forces in the two strands above it so that the resultant force on the junction is zero. The two sloping strands are perpendicular, and we have chosen the x and y directions to be along them. The tension Tx is 0.127 N. Find (a) the tension Ty, (b) the angle the x axis makes with the horizontal, and (c) the angle the y axis makes with the horizontal.
A black widow spider hangs motionless from a web that extends vertically from the ceiling above. If the spider has a mass of 1.5 g, what is the tension in the web?
A car of mass 1 230 kg travels along a circular road of radius 60.0 m at 18.0 m/s. (a) Calculate the magnitude of the cars centripetal acceleration. (b) What is the magnitude of the force of static friction acting on the car? (See Section 7.4.)
A large crate of mass m is placed on the flatbed of a truck but not tied down. As the truck accelerates forward with acceleration a, the crate remains at rest relative to the truck. What force causes the crate to accelerate? (a) the normal force (b) the gravitational force (c) the friction force (d) the ma force exerted by the crate (e) No force is required.
Why is the following situation impossible? A book sits on an inclined plane on the surface of the Earth. The angle of the plane with the horizontal is 60.0. The coefficient of kinetic friction between the book and the plane is 0.300. At time t = 0, the book is released from rest. The book then slides through a distance of 1.00 m, measured along the plane, in a time interval of 0.483 s.
Which of the following is impossible for a car moving in a circular path? Assume that the car is never at rest. (a) The car has tangential acceleration but no centripetal acceleration. (b) The car has centripetal acceleration but no tangential acceleration. (c) The car has both centripetal acceleration and tangential acceleration.
A woman uses a rope to pull a block of mass m across a level floor at a constant velocity. The coefficient of kinetic friction between the block and the floor is k. The rope makes an angle with the floor. Find an algebraic expression for the tension in the rope in terms of the parameters listed in the problem and any constants.
A string under a tension of 50.0 N is used to whirl a rock in a horizontal circle of radius 2.50 m at a speed of 20.4 m/s on a fricitonless surface as shown in Figure P6.25. As the string is pulled in, the speed of the rock increases. When the string on the table is 1.00 m long and the speed of the rock is 51.0 m/s, the string breaks. What is the breaking strength, in newtons, of the string? Figure P6.25
Why is the following situation impossible? A book sits on an inclined plane on the surface of the Earth. The angle of the plane with the horizontal is 60.0. The coefficient of kinetic friction between the book and the plane of 0.300. At time t = 0, the book is released from rest. The book then slides through a distance of 1.00 m, measured along the plane, in a time interval of 0.483 s.
A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop (Fig. P5.22). The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure the cars remain on the track. The biggest loop is 40.0 in high. Suppose the speed at the top of the loop is 13.0 m/s and the corresponding centripetal acceleration of the riders is 2g. (a) What is the radius of the arc of the teardrop at the top? (b) If the total mass of a car plus the riders is M, what force does the rail exert on the car at the top? (c) Suppose the roller coaster had a circular loop of radius 20.0 m. If the care have the same speed, 13.0 m/s at the top, what is the centripetal acceleration of the riders at the top? (d) Comment on the normal force at the top in the situation described in part (c) and on the advantages of having teardrop-shaped loops.