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# Work

Work transfers energy to a system through the forceful manipulation of its state. Do some work on yourself to master this fundamental mode of energy transfer.

# Work 2D - Problem Solving

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

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

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

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

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

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

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

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

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

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