How Does a Block of Ice Move When Sliding Off a Sloped Roof?

[brundlfly]

Homework Statement

A block of ice starts from rest on an apartment building’s roof, which slopes at 41° below the horizontal. The block slides down the icy frictionless roof for 5.0 m and then leaves the edge, which is 12 m above the ground.
a. How far from the building does the block strike the ground?
b. If a 1.8 m fence stands 6.0 m from the building, show whether or not the ice block will hit the fence.

Homework Equations

The Attempt at a Solution

I figured since the ice block starts from rest the initial velocity is 0; the x component of the rooftop vector is 5*cos(-41) = 3.77 and the y component is 5*sin(-41) = -3.28. I struggle with finding a way to find the final velocity when the ice block leaves the rooftop. My goal was to use the point where the block leaves the rooftop as origin and the 12m as my negative y-axis to calculate the trajectory which will answer part a and b. Can I use r_f = r_i + v_i * t + 1/2 * g * t^2 to get the time? I solved for t and got t = 5m + 1/2(-9.8) = 9.9s but I am not sure if this is right. I would appreciate your support.

Thanks.

 

[voko]

Your approach is not correct. You assume that the acceleration of the block is g as it slides down; but that is not true, because the block is not acted upon only by gravity, it also feels the normal force from the roof. So you should set up a FBD and find the resultant force and hence the acceleration.

Alternatively, you could use conservation of energy.

 

[Yosty22]

Voko makes a good point. If you do set it up correctly, conservation of energy can work quite well. If not, make sure you draw a free body diagram, both when it is on the roof and after it leaves the roof. You were correct in thinking the downward acceleration is gravity, BUT only after it leaves the roof and it enters free fall.

 

[brundlfly]

Your approach is not correct. You assume that the acceleration of the block is g as it slides down; but that is not true, because the block is not acted upon only by gravity, it also feels the normal force from the roof. So you should set up a FBD and find the resultant force and hence the acceleration.

Alternatively, you could use conservation of energy.

The thing is that it is an introductory course in Physics and conversion of energy hasn't been dealt with yet, the exercise is in context of 2D motion. I am just thinking would the speed not be the magnitude of the 5m vector in the -y axes and in the +x axis be the initial point of the free fall so V_0; since V_o is the only thing I need, right?

 

[Yosty22]

Without energy, you should think of terms of free fall. Remember, when it has entered free fall, it already has an initial velocity (how fast it is going at the bottom of the room before it starts falling). It might be best to break it down into two problems. One as it goes from the top of the roof to the bottom of the roof and one from the bottom of the roof to the ground.

 

[voko]

The motion on the roof is 1D. But you have to figure out the acceleration - use FBD as indicated earlier.

When the block leaves the roof, it is 2D.