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## 2D Dynamics

With 2D dynamics, we can explain the orbit of the planets around the Sun, the grandfather clock, and the perfect angle to throw a snowball to nail your nemesis as they run away from you.

# Motion along Inclined Planes

In the figure above, the inclined plane makes a $$30^\circ$$ angle with the horizontal. The masses of crates $$A$$ and $$B$$ are $$m_A=80\text{ kg}$$ and $$m_B=x\text{ kg},$$ respectively. The coefficient of kinetic friction at the surface of the inclined plane is $$\mu=\frac{\sqrt{3}}{10},$$ and the pulley is frictionless. If crate $$A$$ is sliding up the ramp at a constant speed, what is the value of $$x?$$

A block slides down an inclined plane that makes a $$45^\circ$$ angle with the floor. If the coefficient of kinetic friction is $$\mu=\frac{1}{19},$$ what is the acceleration of the block?

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

A coin slides down a ramp angled at $$30^\circ$$ with respect to the horizontal. If the coin starts from rest, what is its speed in m/s after sliding $$1~\mbox{m}$$?

Details and assumptions

• The ramp is frictionless.
• The acceleration of gravity is $$-9.8~\mbox{m/s}^2$$.

In the figure above, the inclined plane makes an angle $$\theta$$(in radians) with the horizontal. The masses of crates $$A$$ and $$B$$ are $$m_A=17\text{ kg}$$ and $$m_B=6\text{ kg},$$ respectively. If the ramp is perfectly frictionless, and crate $$A$$ slides down the ramp at a constant speed, what is the value of $$\sin\theta?$$

A block slides down a frictionless, inclined plane that makes a $$30^\circ$$ angle with the floor. If the block is initially at rest, and the length of the inclined plane is $$d=15\text{ m},$$ how many seconds does it take for the block to reach the end of the plane?

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

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