Classical Mechanics

# 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?

×