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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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