A block of mass m is initially at rest on a frictionless horizontal plane surface. At time t-0, a decreasing force given by F = Foet is applied on the block, where a is a constant. Find the expression of the position x(t) of the block as a function of time.

A force F is applied to a block to move it up a θ = 27° inclined frictionless surface. If F = 72 Newton, and M =4.2 kg, what is the magnitude of the acceleration of the block?

A block of mass m = 0.5 kg is kicked so that it slides up a ramp inclined at an angle θ = 30°. At the bottom of the ramp, the block has speed v0 = 4.0 m/s. There is a coefficient of kinetic friction between the block and ramp µK = 0.18. (a) How far up the ramp does the block slide? (b) Assume that the block comes to rest and does not slide back down the ramp. What must be the minimum coefficient of static friction between the block and ramp?

A hockey puck is struck by two sticks at the same time at 90° angles to each other. One stick struck with 30 N of force in the positive y direction. The other stick struck with 45 N of force in the positive x direction. Find the magnitude and angle of the resultant force on the hockey puck.

A block of mass m rests on a plane inclined an angle with the horizontal. A spring with force constant k is attached to the block. The coefficient of static friction between the block and plane is  s. The spring is pulled upward along the plane very slowly. (a) What is the extension of the spring the instant the block begins to move? (b) The block stops moving just as the extension of the contracting spring reaches zero. Express k (the kinetic coefficient of friction) in terms of s and .

A block lies on a plane raised an angle θ from the horizontal. Three forces act upon the block: F→w, the force of gravity: F→n, the normal force; and F→f, the force of friction. The coefficient of friction is large enough to prevent the block from sliding. Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system b. Because the block is not moving, the sum of the x components of the forces acting on the block must be zero. Find an expression for the sum of the x components of the forces acting on the block, using coordinate system b. To find the magnitude of the normal force, you must express Fn in terms of Fw since Ff is an unknown. Using the equations you found in the two previous parts, find an expression for Fn involving Fw and θ but not Ff.

A parachutist whose mass is 75 kg drops from a helicopter hovering 2500 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b₁ = 20 N-sec/m when the chute is closed and b₂ = 100 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 30 m/sec, after how many seconds will the parachutist reach the ground? Assume that the acceleration due to gravity is 9.81 m/sec². The parachutist will reach the ground after (Round to two decimal places as needed.) seconds.