What Is the Minimum Speed Needed for a Boulder to Clear the Dam?

In summary, the minimum speed required for the 76 kg boulder to travel from the top of a 20m cliff to a level plain 25 m below a dam, without striking the dam, is 50 m/s. This is found by calculating the time it takes for the boulder to fall from the cliff (2.02 seconds), the horizontal distance it travels during that time (100 m), and the height it falls during that time (49.5 m).
  • #1
Bottomsouth
27
0

Homework Statement



a 76 kg boulder is rolling horizontally at a top of a vertical cliff that is 20m above the surface of a lake. the top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the surface of the water in the lake. a level plain is 25 m below the top of the dam. what must the minimum speed of the rock be just as it leaves the cliff so that it will travel to the plain without striking the dam?

Homework Equations





The Attempt at a Solution



20= 4.9 * t^2
20/4.9= t^2
t=square 20/49
t=2.02

100 = vx0 * t
100/2.02 = vx0
vx0 = 45.45 m/s

20+25 = .5 * 9.8 * t^2
45 = 4.9* t^2
t+3.03

V0x * 3.3 = 150m
45.45*3.3 = 150
150-100 = 50m

I am not getting the min speed. Is it the 45.45? I believe so, but the program doesnt. Appreciate any help. The 50 m is correct.
 
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  • #2
Bottomsouth said:
20= 4.9 * t^2
20/4.9= t^2
t=square 20/49
t=2.02

100 = vx0 * t
100/2.02 = vx0
vx0 = 45.45 m/s
Redo that last bit of arithmetic.
 
  • #3
49.5, thanks. Have had very little sleep.
 

Related to What Is the Minimum Speed Needed for a Boulder to Clear the Dam?

1. What is the minimum speed required for a boulder to start rolling?

The minimum speed required for a boulder to start rolling depends on various factors, such as the size and weight of the boulder, the slope of the surface it is resting on, and the friction between the boulder and the surface. In general, a boulder needs to be pushed or pulled at a speed that is greater than its static friction with the surface in order to start rolling.

2. What is the formula for calculating the minimum speed for a boulder to start rolling?

The formula for calculating the minimum speed for a boulder to start rolling is v = √(2μgd), where v is the minimum speed, μ is the coefficient of static friction between the boulder and the surface, g is the acceleration due to gravity, and d is the diameter of the boulder.

3. How does the slope of the surface affect the minimum speed for a boulder to start rolling?

The steeper the slope of the surface, the lower the minimum speed required for a boulder to start rolling. This is because a steeper slope increases the component of the force of gravity that acts parallel to the surface, making it easier for the boulder to overcome its static friction and start rolling.

4. Can the minimum speed for a boulder to start rolling change?

Yes, the minimum speed for a boulder to start rolling can change depending on factors such as the surface conditions (e.g. wet vs dry), the shape and weight of the boulder, and the angle of the slope. A rougher surface or a heavier boulder may require a higher minimum speed to start rolling, while a smoother surface or a lighter boulder may require a lower minimum speed.

5. Is it possible for a boulder to start rolling without any external force?

No, a boulder cannot start rolling without any external force. This is because the force of gravity alone is not enough to overcome the static friction between the boulder and the surface. Therefore, an external force (such as a push or pull) is required to initiate the motion of the boulder.

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