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
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- 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_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_forwardA small block slides down a frictionless track whose shape is described by y = (x^2) /d for x<0 and by y = -(x^2)/d for x>0. The value of d is 4.74 m, and x and y are measured in meters as usual. Now suppose the blocks starts on the track at x = 2.39 m. The block is given a push to the left and begins to slide up the track, eventually reaching its maximum height at x = 0, at which point it turns around and begins sliding down. What was its initial speed in this case? 6.74 m/s 4.86 m/s 3.44 m/s 4.98 m/sarrow_forward
- A small object is placed at the top of an incline that is essentially frictionless. The object slides down the incline onto a rough horizontal surface, where it stops in 5.0 s after traveling 60 m. (a) What is the speed of the object at the bottom of the incline and its acceleration along the horizontal surface? (b) What is the height of the incline?arrow_forwardA skier starts going down a rocky hill that is inclined 30 degrees from the horizontal. It is 2 km long, and he starts with an initial speed of 5 m/s down the hill. If the coefficient of kinetic friction between his skis and the hill is 0.7: Does he make it to the bottom? If so, how long does it take?arrow_forwardA 3kg block slides along a floor with coefficient of kinetic friction µk = 0.3, initially moving at 7.0m/s. It %3D travels for 2.0 meters, then encounters a ramp sloped upward at 40°. The ramp also has a coefficient of kinetic frictionuk = 0.3. How fast is the block moving when it reaches the bottom of the ramp? How far %3D up the ramp does the block slide, before momentarily coming to rest? 1) Draw a pictoriolarrow_forward
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- 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