Work 2D - Problem Solving

         

A mass m=3 kg m = 3 \text{ kg} that lies on a horizontal surface is connected to another mass M=6 kg, M = 6 \text{ kg}, as shown in the above diagram. The coefficient of kinetic friction between mass mm and the surface is μk=0.1. \mu_k = 0.1. If the system is released from rest, what is the squared velocity of mass m, m , when mass M M as descended a distance of h=9 m? h = 9 \text{ m}?

The gravitational acceleration is g=10 m/s2. g= 10 \text{ m/s}^2 .

An object of mass m=8 kg m = 8 \text{ kg} moves on a frictionless horizontal plane with a velocity (in meters per second) of v=15i^+20j^. \vec{v} = 15 \hat{i} + 20 \hat{j}.

If a force (in Newtons) of F=4i^ \vec{F} = 4 \hat{i} is applied to the object for 8 8 seconds, how much work does this force do to the object?

An escalator is moving downward at a constant speed of u=3 m/s. u = 3 \text{ m/s}. A man of mass m=46 kg m = 46 \text{ kg} is running upwards on it at a constant speed of v=6 m/s. v =6 \text{ m/s}. If the height of the escalator is h=2 m, h =2 \text{ m}, how much work does the man do while he runs up the escalator?

A squirrel of mass m=12 kg m =12 \text{ kg} slides up an inclined plane that makes a θ=45 \theta = 45^\circ angle with the horizontal, with an initial velocity of v=6 m/s. v = 6 \text{ m/s}. If the coefficient of kinetic friction between the plane and the squirrel's feet is μ=0.5, \mu = 0.5, how much work does friction do to the squirrel until he comes to a stop?

The gravitational acceleration is g=10 m/s2. g= 10 \text{ m/s}^2.

A mass m=4 kg m = 4 \text{ kg} that lies on a frictionless horizontal surface is connected to another mass M=5 kg M = 5 \text{ kg} by a string, as shown in figure above. If the system is released from rest, what is the squared velocity of mass m, m, when mass M M has descended a distance of h=18 m? h = 18 \text{ m}?

The gravitational acceleration is g=10 m/s2. g= 10 \text{ m/s}^2 .

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