Concept explainers
A basin surrounding a drain has the shape of a circular cone opening upward, having everywhere an angle of 35.0° with the horizontal. A 25.0-g ice cube is set sliding around the cone without friction in a horizontal circle of radius R. (a) Find the speed the ice cube must have as a function of R. (b) Is any piece of data unnecessary for the solution? Suppose R is made two times larger. (c) Will the required speed increase, decrease, or stay constant? If it changes, by what factor? (d) Will the time interval required for each revolution increase, decrease, or stay constant? If it changes, by what factor? (e) Do the answers to parts (c) and (d) seem contradictory ? Explain.
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Chapter 6 Solutions
Physics for Scientists and Engineers
- A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position x along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data. (b) Determine the acceleration of the cart from the slope of this graph. (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 4.3.arrow_forwardIn a "crazy elevator ride" at the amusement park, a 300 kg "elevator car" slides vertically down a frictionless shaft and curves onto a horizontal section, descending a total height of 25 m. On the horizontal section is a friction pad designed to bring the car to rest. If the coefficient of friction between the car and the pad is μk=0.4, how long in meters does the pad need to be to stop the car?arrow_forwardA 1 kg Box slides down an inclined plane. It has an incline of 1.25664 radians and coefficient of kinetic friction of 0.44. What is the final speed of the Box if it started at rest and the change in height is 4 m? V =arrow_forward
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- In the figure, a 4.2 kg block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed is vo = 5.1 m/s, the height difference is h = 1.0 m, and μk = 0.632. Find d. Number i Units d μ= 0- h - Мнarrow_forwardAn unattended car of mass 1449 kg starts sliding down a 29.6 degree angle street. If the coefficient of friction is 0.21, how fast is the car traveling when it reaches the bottom of the 66.1 m long hill?arrow_forwardIn the figure, a 4.2 kg block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed is vo = 7.1 m/s, the height difference is h = 1.2 m, and u = 0.594. Find d. u= 0- Number Unitsarrow_forward
- A 12 kg box is released from the top of an incline that is 5 m long and makes an angle of 40 degrees to the horizontal. The friction force between the box and the incline is 60 N. What is the coecient of kinetic friction µk between the box and the incline?arrow_forwardA 1,550 kg roller coaster cart is pulled at a constant speed of 4.3 m/s to the top of a 53.5 m tall ramp that has a 45° incline. The coefficient of friction between the ramp and the roller coaster cart is μ = 0.052. u When the roller coaster cart makes it to the top of the ramp, the cable suddenly breaks and the roller coaster cart accelerates back down to the bottom of the ramp. ไปป FA tow cable 53.5 m Calculate the work done by friction on the roller coaster cart as it rolled back down the ramp after the cable broke. kJ Write your answer to three significant figures.arrow_forwardOne non-powered sled is sliding over a snowed surface, first down from the top of a flat and inclined plane using only gravity and no initial speed and then it continues to move along a horizontal surface until a full stop. The plane’s surface is inclined with 45 degrees relative to the horizontal. The top of the inclined plane is 2 meters high relative to the same horizontal surface. The friction coefficient between the sled and snow is 0.05 on all surfaces. Determine the formula and the value for the distance made by the sled onto the horizontal surface.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning