Concept explainers
(a)
The time taken by the runaway ski to slide down a 250-m long slope when the coefficient of kinetic friction between the ski and the snow is 0.100.
Answer to Problem 81QAP
The time taken by the runaway ski to slide down a 250-m long slope when the coefficient of kinetic friction between the ski and the snow is 0.100 is 8.12 s.
Explanation of Solution
Given:
The length of the ski slope
The angle made by the slope to the horizontal
Initial speed of the ski
Coefficient of kinetic friction between the ski and snow
Formula used:
A free body diagram of the ski is drawn to analyze its motion.
Assume a coordinate system, with the +x directed downwards along the incline and +y directed upwards, perpendicular to the incline. The weight
Resolve the weight
The ski is in equilibrium along the y direction.
Therefore,
Therefore, using equation (1),
The force of kinetic friction and the normal force are related according to the following equation:
From equation (2)
Write the force equation along the +x direction.
Use the values of wx and fk from equations (2) and (3) in the expression,
Simplify and write an expression for ax.
Use the following equation of motion to obtain the value of the time t.
Calculation:
Substitute the values of the variables in equation (4) and calculate the value of the acceleration.
Use the calculated value of ax and the values of v0 and
Solve the quadratic equation.
Taking the positive root,
Conclusion:
The time taken by the runaway ski to slide down a 250-m long slope when the coefficient of kinetic friction between the ski and the snow is 0.100 is 8.12 s.
(b)
The time taken by the runaway ski to slide down a 250-m long slope when the coefficient of kinetic friction between the ski and the snow is 0.150.
Answer to Problem 81QAP
The time taken by the runaway ski to slide down a 250-m long slope when the coefficient of kinetic friction between the ski and the snow is 0.150 is 8.39 s.
Explanation of Solution
Given:
The length of the ski slope
The angle made by the slope to the horizontal
Initial speed of the ski
Coefficient of kinetic friction between the ski and snow
Formula used:
The acceleration of the ski down the slope is given by
The time taken to reach the bottom of the slope is calculated using the expression,
Calculation:
Substitute the values of the variables in equation for acceleration and calculate the value of the acceleration.
Use the calculated value of ax and the values of v0 and
Solve the quadratic equation.
Taking the positive root,
Conclusion:
The time taken by the runaway ski to slide down a 250-m long slope when the coefficient of kinetic friction between the ski and the snow is 0.150 is 8.39 s.
Want to see more full solutions like this?
Chapter 5 Solutions
COLLEGE PHYSICS
- If you press a book flat against a vertical wall with your hand, in what direction is the friction force exerted by the wall on the book? (a) downward (b) upward (c) out from the wall (d) into the wall.arrow_forwardPROBLEM 3 The 4250-lb automobile shown in Figure travels down the 10° inclined road at a speed of 20 ft/s. If the driver jams on the brakes. causing his wheels to lock determine how far s the tires skid on the road. The coefficient of kinetic friction between the wheels and the road is μk 0.75. PROBLEM 4 110⁰ 20 ft/s SULT For a short time the crane in Fig. 6-7 lifts the 3.75 Mg bear with a force of F(8-282) kN, Determine the speed of the bearn when it has risen s 5 marrow_forwardIn a pickup game of dorm shuffleboard, students crazed by final exams use a broom to propel a calculus book along the dorm hallway. If the 3.5 kg book is pushed from rest through a distance of 0.83 m by the horizontal 31 N force from the broom and then has a speed of 1.0 m/s, what is the coefficient of kinetic friction between the book and floor? Number Unitsarrow_forward
- 19:49 Sat 14 May * 77% T For question 14 to 18: A child is on a toboggan (a system of +x total mass m ) accelerates down a hill of length L inclined at an angle 0 to the horizontal in a time interval At. For question 14 to 18, ignore friction unless it is specified otherwise 17. If the child starts from rest and accelerates uniformly down the hill, the time required to reach the bottom of the hill is ... 2L a) Lg sin 0 b) 2Lg sin 0 21g sine c) d) g sin 0arrow_forward**.59 SSM ILW In Fig. 6-45, a 1.34 kg ball is connected by means of two massless strings, each of length L = 1.70 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.70 m and are taut. The tension in the upper string is 35 N. What are the (a) tension in the Rotating rod lower string. (b) magnitude of the net force Feet on the ball, and (c) speed of the ball? (d) What is the di- rection of Faet? Flg. 6-45 Problem 59.arrow_forward5) A 640-N hunter gets a rope around a 3200-N polar bear. They are initially stationary, 20 meters apart, on frictionless level ice. The hunter now pulls on the rope such that she and the polar bear slide closer together. This continues until they eventually meet at some point on the ice. What total distance will the polar bear have slid? a) 1.0 m b) 3.3 m c) 10 m d) 12 m e) 17 marrow_forward
- *•26 00 Figure 6-32 shows three crates being pushed over a concrete floor by a horizontal force F of magnitude 440 N. The masses of the crates are m, = 30.0 kg, m2 = 10.0 kg, and m3 = 20.0 kg. The coeffi- cient of kinetic friction between the floor and each of the crates is 0.700. (a) What is the magnitude F of the force on crate 3 from crate 2? (b) If the crates then slide onto a polished floor, where the coefficient of kinetic friction is less than 0.700, is magni- tude F more than, less than, or the same as it was when the coefficient was 0.700? Fig. 6-31 Problem 25. %3D Flg. 6-32 Problem 26. Frictionless, massless pulleyarrow_forward3.- A truck tows a 400 kg log from a ditch by means of a winch attached to its rear part. Knowing that the winch applies a constant force F and the coefficient of kinetic friction between the ground and the log is 0.5, determine the force F if the log reaches a speed of 0.5 m / s in 1.8 s. Visual representation (Make drawings or diagrams, clearly indicate the vectors and variables involved in the problem, it can be on the drawing)arrow_forward112. " Consult Multiple-Concept Example 10 for insight into solving this type of problem. A box is sliding up an incline that makes an angle of 15.0° with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is 0.180. The initial speed of the box at the bottom of the incline is 1.50 m/s. How far does the box travel along the incline before coming to rest?arrow_forward
- •14 Go Figure 7-27 shows an over- head view of three horizontal forces acting on a cargo canister that was initially stationary but now moves -х across a frictionless floor. The force magnitudes are F = 3.00 N, F = 4.00 N, and F; = 10.0 N, and the indi- cated angles are 0, = 50.0° and 0 = в, %3! 35.0°. What is the net work done on Figure 7-27 Problem 14. the canister by the three forces dur- ing the first 4.00 m of displacement?arrow_forward•7 A 3.0 kg body is at rest on a frictionless horizontal air track when a constant horizontal force F acting in the positive direction of an x axis along the track is applied to the body. A stroboscopic graph of the position of the body as it slides to the right is shown in Fig. 7- 25. The force F is applied to the body at t = 0, and the graph records the position of the body at 0.50 s intervals. How much work is done on the body by the applied force F between t = 0 and t= 2.0 s? rt%=0 0.5 s -1.0s 1.5 s 2.0 s 0.2 0.4 0.6 0.8 x (m)arrow_forward3/47 The small 0.6-kg block slides with a small amount of friction on the circular path of radius 3 m in the ver- tical plane. If the speed of the block is 5 m/s as it passes point A and 4 m/s as it passes point B, deter- mine the normal force exerted on the block by the surface at each of these two locations. 30° B 3 m A Problem 3/47arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning