Impulse of a variable force


A crate of mass \(2\text{ kg}\) lies at rest on a floor. The coefficient of static friction between the crate and floor is \(\mu_s=0.3,\) and that of kinetic friction between the crate and floor is \(\mu_k=0.1.\) If a horizontal force \(F\) is applied on the crate, and the magnitude of the force changes with respect to time \(t\) according to the equation \(F=3t\) in unit of N, what is the speed of the crate after four seconds?

Assume that gravitational acceleration is \(g=10\text{ m/s}^2.\)

A crate of mass \(2.6\text{ kg}\) is initially at rest on a frictionless inclined plane that makes a \(30^\circ\) angle with the horizontal. A force \(F\) whose magnitude is \(F=(18-t)\text{ N}\) with respect to time \(t\) is exerted on the crate for five seconds in the direction up the plane. Find the approximate resulting velocity of the crate.

Assume that gravitational acceleration is \(g=10\text{ m/s}^2.\)

An object of mass \(2\text{ kg}\) is moving on a frictionless horizontal floor with a velocity of \(1.4\text{ m/s},\) in a straight line. If two consecutive forces \(F_1=2\text{ N}\) and \(F_2=-6\text{ N}\) are applied on the object for \(7\) and \(8\) seconds each, respectively, what is the resulting velocity of the object?

An airplane of mass \(5000\text{ kg}\) is flying straight at a constant speed of \(70\text{ m/s}.\) A head wind starts to blow, and the force exerted by the wind increases \(50\text{ N}\) in magnitude every second. If the plane propels itself at a constant power, how much speed will the plane lose after ten seconds?

An object of mass \(5\text{ kg},\) initially at rest, is pushed by a force \(F\) of duration \(1\text{ s}\) whose strength varies with time according to the graph above. If \(a=4,\) what is the resulting speed of the object?


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