A block of mass M and contact area A slides on a thin film of oil with thickness h as shown in the figure. When released, a mass m exerts tension on the cord, causing the block to accelerate. (a) Neglect friction in the pulley and air resistance, and develop an algebraic expression for the viscous force that acts on the block when it moves at a speed V. (b) Derive a differential equation for the block speed as a function of time, and obtain an expression for the block speed as a function of time. (c) For the values μ = 0.04 Pa−s, m = 2 kg, A = 10 cm2, and h = 0.1 mm, determine the block mass M if it takes 10 s for the block speed to reach 1 m/s.
A sailboat race course consists of four legs, defined by the displacement vectors A→, B→, C→, and D→, as the drawing indicates. The magnitudes of the first three vectors are A = 3.70 km, B = 4.70 km, and C = 4.60 km. The finish line of the course coincides with the starting line. Using the data in the drawing, find (a) the distance of the fourth leg and (b) the angle θ. (a) Number Units (b) Number Units
The three displacement vectors in the drawing have magnitudes of A = 4.15 m, B = 5.45 m, and C = 4.42 m. Find the resultant ((a) magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis which is less than 90∘. (a) Number Units (b) Number Units
The figure shows a two-dimensional vector A→. The x-component of A→ is -9.25 and the y-component is 6.60. What is the magnitude A of this vector? A =
Starting from a location with position vector r1,x = −15.1 m and r1,y = 25.7 m, a rabbit hops around for 11.9 seconds with average velocity vav,x = −2.23 m/s and vav,y = 1.39 m/s. Determine the components r2,x and r2,y of the position vector of the rabbit's final location. r2,x = m r2,y = m
The route followed by a hiker consists of three displacement vectors A→, B→, and C→. Vector A→ is along a measured trail and is 1510 m in a direction 21.0∘ north of east. Vector B→ is not along a measured trail, but the hiker uses a compass and knows that the direction is 17.0∘ east of south. Similarly, the direction of vector C→ is 32.0∘ north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A→ + B→ + C→ = 0. Find the magnitudes of (a) vector B→ and (b) vector C→. (a) Number Units (b) Number Units