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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.

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 \( g= 10 \text{ m/s}^2 . \)

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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?

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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 \( g= 10 \text{ m/s}^2. \)

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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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