How Does Incline Angle Affect Ice Block Acceleration on a Frictionless Ramp?

In summary, A block of ice with mass m is released from rest at the top of a frictionless ramp with length L. The ice reaches a speed of v1 at the bottom of the incline. Using this information, we can determine the time it takes for the ice to hit the bottom, the angle between the ramp and the horizontal, and the acceleration of the ice. To calculate the time, we use the formula T = 2L / v1. To find the angle, we need to consider the coordinate system being slanted at the angle of the ramp. Lastly, the acceleration of the ice is found using the formula A = v1^2 / 2L.
  • #1
oreosama
51
0
A block of ice of mass m is released from rest at the top of a frictionless ramp of length L. at the bottom of the incline the speed of the ice is v1. given m,L,v1 determine

the time needed to hit the bottom
the angle between the ramp and the horizontal
the accel of the ice

I made my coordinate system slant at the angle of the ramp because I thought this would make it less work

http://i.imgur.com/d18GN.png

(is this okay?)



x0 = 0
x = L
v0 = 0
v = v1
a= A
t = T

v1 = 0 + AT

T = v1/A

v1^2 = 2AL

A = v1^2 / 2L

T = v1 / (v1^2 / 2L)

T = 2L / v1

I got these answers pretty cleanly but I have no idea what I should be doing to get theta since I don't see a way to get the lengths of the potential triangle with hypoteneus L
 
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  • #2
What is the acceleration of the ice if it is dropped from rest, free fall?
If it has to follow the ramp inclination, what is it's acceleration?
 

Related to How Does Incline Angle Affect Ice Block Acceleration on a Frictionless Ramp?

1. What is a block of ice?

A block of ice is a solid state of water, typically formed by freezing water in a container or natural body of water.

2. How does a block of ice form?

A block of ice forms when the temperature of water drops below its freezing point of 32°F (0°C). The molecules of water slow down and form a crystalline structure, creating a solid block of ice.

3. What forces act on a block of ice?

The main forces acting on a block of ice are gravity, buoyancy, and friction. Gravity pulls the block of ice towards the center of the earth, buoyancy exerts an upward force on the ice due to the water it displaces, and friction can cause the ice to slide or melt depending on the surface it is on.

4. How does the weight of a block of ice affect its stability?

The weight of a block of ice affects its stability by increasing the force of gravity on the ice. This can cause the ice to sink or break if it is not supported by the water it is floating in.

5. Can a block of ice exert a force on other objects?

Yes, a block of ice can exert a force on other objects through collisions or by melting and transferring its energy to the other object. This can be observed in ice hockey, where the puck is pushed by the stick and slides on the ice, which creates a force on the puck.

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