Motion along Inclined Planes

         

In the figure above, the inclined plane makes a 3030^\circ angle with the horizontal. The masses of crates AA and BB are mA=80 kgm_A=80\text{ kg} and mB=x kg,m_B=x\text{ kg}, respectively. The coefficient of kinetic friction at the surface of the inclined plane is μ=310,\mu=\frac{\sqrt{3}}{10}, and the pulley is frictionless. If crate AA is sliding up the ramp at a constant speed, what is the value of x?x?

A block slides down an inclined plane that makes a 4545^\circ angle with the floor. If the coefficient of kinetic friction is μ=119,\mu=\frac{1}{19}, what is the acceleration of the block?

The gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

A coin slides down a ramp angled at 3030^\circ with respect to the horizontal. If the coin starts from rest, what is its speed in m/s after sliding 1 m1~\mbox{m}?

Details and assumptions

  • The ramp is frictionless.
  • The acceleration of gravity is 9.8 m/s2-9.8~\mbox{m/s}^2.

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

A block slides down a frictionless, inclined plane that makes a 3030^\circ angle with the floor. If the block is initially at rest, and the length of the inclined plane is d=15 m,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 m/s2.g=10\text{ m/s}^2.

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