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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 1D - Problem Solving

A body of mass $$m = 2 \text{ kg}$$ is dropped from $$h = 70 \text{ cm}$$ above a horizontal platform that is fixed to one end of an elastic spring, as shown in the figure above. As a result the spring is compressed by an amount of $$\Delta x = 20 \text{ cm}.$$ What is the spring constant of the spring?

The gravitational acceleration is $$g= 10 \text{ m/s}^2$$ and the air resistance is negligible.

A body initially at rest is dropped from a height of $$h = 45\text{ m}.$$ If the coefficient of restitution is $$e= 0.6,$$ what is the height the body reaches at the second bounce?

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

A $$14$$-meter-long rod of mass $$2 \text{ kg}$$ with homogeneous density is standing vertically with one end on a horizontal floor. Find the gravitational potential energy of the rod.

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

A body of mass $$m = 5 \text{ kg}$$ is moving on a frictionless horizontal plane with a velocity of $$v= 4 \text{ m/s}.$$ The body is heading to the vertical platform fixed to one end of an elastic spring, as shown in figure above. As a result the spring is compressed by an amount of $$\Delta x = 20 \text{ cm}.$$ What is the spring constant of the spring?

A block of mass $$m_1 = 3 \text{ kg}$$ is moving on a frictionless horizontal surface with a velocity of $$u_1 = 16 \text{ m/s}$$ towards another block of mass $$m_2 = 9 \text{ kg}$$ that is moving on the same surface with a velocity of $$u_2 = 8 \text{ m/s}$$ in the same direction. A massless spring of spring constant $$k = 36 \text{ N/m}$$ is attached to $$m_2$$ as shown in figure above. When block $$m_1$$ collides with the spring, what is the maximum change in the spring's length?

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