A mass is an initial speed of v down a ramp inclined at an angle of θ to the horizontal. The coefficient of kinetic friction between the ramp and the mass is μ. After sliding a distance d down the ramp, the mass slides onto a frictionless horizontal surface and encounter a spring which it compresses a distance x. determine the spring constant, in term of given quantities

A package is projected up a 15° incline at A with an initial velocity of 8 m/s. Knowing that the coefficient of kinetic friction between the package and the incline is 0.12, determine (a) the maximum distance d that the package will move up the incline, (b) the velocity of the package as it retums to its original position. 10 m B 15°

A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28 degree incline. After sliding down the 110-m-long incline (on which the coefficient of kinetic friction is μk= 0.17), the snowboarder has attained a velocity v. The snowboarder then slides along a flat surface (on which μk= 0.14) and comes to rest after a distance x.  Determine BOTH the snowboarder's acceleration on the incline AND his acceleration on the flat surface. Then, determine x.

A mass M = 12.0 kg is pulled up an incline plane by a F = 170 N. The plane angle is 30o with respect to the horizontal. The kinetic coefficient of friction between the surfaces is  μ = 0.40. Calculate the acceleration of the block

A 20-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 28 N. Starting from rest, the sled attains a speed of 2.6 m/s in 9.4 m. Find the coefficient of kinetic friction between the runners of the sled and the snow.

Two blocks are connected by a massless rope over a massless, frictionless pulley, as shown in the figure. The mass of block 2 is m2 12.1 kg, and the coefficient of kinetic friction 0.200. The angle 0 of between block 2 and the incline is µk the incline is 33.5°. If block 2 is moving up the incline at 2 constant speed, what is the mass mj of block 1? 1 kg M¡ =

Imagine a skydiver with a mass of m jumping out of an airplane at an altitude of h. As the skydiver descends, they experience two forces: air resistance and gravity. The force of air resistance varies with time and is described by the following function, where t is the time in seconds since t e skydiver has jumped: vec 2 (F)(t) = (0.5t)ha (x) + (0.11 +0.3t)hat(y) a) Create a air free body diagrar for the skydiver at t = 2 seconds. b) - What is the net for e acting on the skydiver at t = 2 seconds? c) What i the magnitude of the acceleration of the skydiver at t = 2 seconds? Imagine a skydiver with a mass of m jumping out of an airplane at an altitude of h. As the skydiver descends, they experience two forces: air resistance and gravity. The force of air resistance varies with time and is described by the following function, where t is the time in seconds since the skydiver has jumped: Fair (t) = (0.5t)2 + (0.12 + 0.3t)ŷ a) Create a free-body diagram for the skydiver at t = 2 seconds.…

A block, initially at rest, has a mass m and sits on a plane inclined at angle theta. It slides a distance d before hitting a spring and compresses the spring by a maximum distance of xf. If the coefficient of kinetic friction between the plane and block is uk, then what is the force constant of the spring?

A dated box of dates, of mass 7.1 kg, is sent sliding up a frictionless ramp at an angle of e to the horizontal. The figure here gives, as a function of time t, the component Vy of the box's velocity along an x axis that extends directly up the ramp. What is the magnitude of the normal force on the box from the ramp? (m/s) 4 2 (s) -2 Number 64.86 Unit the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Work SHOW HINT e to search 林 10:44 PM ENG 4/4/2021 13 ) 16 17 tohome %23 3 7. W E R. T. 5

A firefighter who weighs 192 lb slides down an infinitely long fire pole that exerts a frictional resistive force with magnitude proportional to her speed with constant of proportionality k. Find her velocity v as a function of t, given that her terminal velocity is -16 ft/s. Assume that she starts from rest. Solve for the solution of this Application of first order differential equation in Dynamics. the final answer is v= -16 (1-e-2t)