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Question about frictionless motion with variable acceleration.

  • #1
1. Person is climbing a mountain with rope attached to rock on a flat surface above for support. The slope has an incline angle of 50 degrees. The rock is on frictionless ground, and the mass of the rope can be ignored. The person (100 kg) is 3 meters from the flat surface, the rock (700 kg) is 6 meters from the edge. What is the minimum acceleration the person needs to climb up at to reach the edge before the rock does. All surfaces are frictionless.



2. I do not know what equations to use :(



3. I attempted by finding the downward acceleration of the person, when he is not moving, and finding that his upward acceleration must be double that.
 

Answers and Replies

  • #2
rude man
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How about writing the equations relating T, the tension in the rope, W, the weight of the man = mg, and N, the force normal to the slope, in both x and y directions?
2 equations, 2 unknowns (T and N).

Remember that T must include the force supporting his upward acceleration
s_double-dot along the slope , where ds = d(x_m)*sec(theta) and theta = 50 deg.
(He starts at s = 0 and winds up hopefully at s = +3m). x_m is the x component of s.

Then, write the corresponding equation for the rock's force and acceleration, involving T, M and x_M where M = mass of rock and x_M is the (negative) distance the rock moves. x_M = 0 for the rock at start of slide and = -6m at time m reaches the top and the rock reaches the edge.

PS - how did you determine that

Then equate time t(s = +3m) = t(x_M = -6m) using the s = 0.5a*t^2 formula.

ps how did you ".... attempt by finding the downward acceleration of the person, when he is not moving, and finding that his upward acceleration must be double that." without knowing what equations to use?
 

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