Concept explainers
A block of mass m is at rest at the origin at t = 0. It is pushed with constant force F0from x = 0 to x = L across a horizontal surface whose coefficient of kinetic friction is µk= µ0(1 −x/L). That is, the coefficient of friction decreases from µ0at x = 0 to zero at x = L
a. Use what you've learned in calculus to prove that
b. Find an expression for the block's speed as it reaches position L.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
- If a single constant force acts on an object that moves on a straight line, the objects velocity is a linear function of time. The equation v = vi + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = vi kx, where k is a constant coefficient and x is the position of the object. Find the law describing the total force acting on this object.arrow_forwardFor t 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: Fnet=mkv2i, where k is a constant. The speed of the object after t = 0 is given by v = vi/(1 + kvit). (a) Find the position x of the object as a function of time. (b) Find the objects velocity as a function of position.arrow_forwardLet us make the (unrealistic) assumption that a boat of mass m gliding with initial velocity v0 in water is slowed by a viscous retarding force of magnitude bv2, where b is a constant, (a) Find and sketch v(t). How long does it take the boat to reach a speed of v0/l000? (b) Find x(t). How far does the boat travel in this time? Let m = 200 kg, v0 = 2 m/s, and b = 0.2 Nm-2s2.arrow_forward
- In the figure, a slab of mass m1 = 40 kg rests on a frictionless floor, and a block of mass m2 = 10 kg rests on top of the slab. Between block and slab, the coefficient of static friction is 0.60, and the coefficient of kinetic friction is 0.40. A horizontal force F→ of magnitude 104 N begins to pull directly on the block, as shown. In unit-vector notation, what are the resulting accelerations of (a) the block and (b) the slab?arrow_forwardIn a shuffleboard game, the puck slides a total of 12 m on a horizontal surface before coming to rest. If the coefficient of kinetic friction between the puck and board is 0.10, what was the initial speed of the puck? 48.5 m/s 4.8 m/s 4.3 m/s 3.8 m/sarrow_forwardThe coefficient of friction between a 33kg exercise mat and the gym floor are us = 0.41 and uk = 0.36. Q-Once the mat is moving, what magnitude of horizontal force will keep it moving at a constant velocity?arrow_forward
- a 2 kg golf ball moves along an x axis according to x(t) = 10t^3 - 2.80t^2 + 7.4t +15 , with x in meters and t in seconds . in unit-vector notation , what is the net force acting on the particle at t= 5.20 s?arrow_forwardThe block has mass m = 6.8 kg, the ramp is at an angle of θ = 28 degrees, the coefficient of kinetic friction between the block and the ramp is μk = 0.25, and the applied force is F = 156.4 N. What is the acceleration of the block up the ramp, in m/s2?arrow_forwardA 0.150 kg particle moves along an x axis according to x(t)=-13.00 + 2.00t - 4.00t2 -3.00t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.40 s?arrow_forward
- Q 5)A force vector F =3i + 3j N is applied on 5 kg mass of body on nonfrictionless horizontal surface. The velocity function of body is v = t + 2 . find the following : 1) frictional force (fs ) 2) the coefficient of friction of surface (μ) . (answer fs =1.7 N , u =0.34)arrow_forwardTarzan, who weighs 820 N, swings from a cliff at the end of a 20.0 m vine that hangs from a high tree limb and initially makes an angle of 22.0 with the vertical. Assume that an x axis extends horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 760 N. Just then, what are (a) the force on him from the vine in unit-vector notation and the net force on him (b) in unit-vector notation and as (c) a magnitude and (d) an angle relative to the positive direction of the x axis? What are the (e) magnitude and (f) angle of Tarzan’s acceleration just then?arrow_forwardA rectangular block of mass 10 kg is allowed to slide down a rough slope which is inclined at an angle of 20. What is the acceleration of the blovk, if the coefficient of the kinetic friction between the block and the slop= 0.15? A. 2 m/s^2 B. 3.5 m/s^2 C. 2.5 m/s^2 D. 3.0 m/s^2 E. 1 m/s^2arrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning