Wile E. Coyote wants to launch Roadrunner into the air using a long lever asshown below. The lever starts at rest before the Coy
ote steps onto one end and pivots around its center of mass. Roadrunner is standing on the other end, which is held up by a small piece of ground underneath. The lever has mass 1.2 kg and length 16 m, the Roadrunner has mass 3.2 kg, and there is no friction at the pivot point of the lever.
a) Draw free body diagrams for the lever, Coyote, and Roadrunner. Make sure to label where all of the forces act on the lever’s free body diagram.
b) What is the minimal mass that Coyote must have to cause the lever to start rotating?
c) The coyote actually has a mass of 18 kg. If the roadrunner goes flying when the lever gets to a 45∘ angle from the horizontal, what is the roadrunner’s speed at that time, assuming the pivot is frictionless?
d) (Optional/challenge) What is the angular acceleration just after Coyote steps onto the lever?
a) Draw free body diagrams for the lever, Coyote, and Roadrunner. Make sure to label where all of the forces act on the lever’s free body diagram.
b) What is the minimal mass that Coyote must have to cause the lever to start rotating?
c) The coyote actually has a mass of 18 kg. If the roadrunner goes flying when the lever gets to a 45∘ angle from the horizontal, what is the roadrunner’s speed at that time, assuming the pivot is frictionless?
d) (Optional/challenge) What is the angular acceleration just after Coyote steps onto the lever?
1 answer:
You might be interested in
Answer:
At 30 degrees, height = 14.39 m and distance = 49.83 m
At 45 degrees, height = 28.77 m and distance = 57.54 m
At 60 degrees, height = 43.16 m and distance = 49.83 m
Explanation:
Let ∝ be the angle with respect to the horizontal that the baseball is hit with.
The horizontal component of the velocity is vcos(∝) and the vertical component of the velocity is vsin(∝).
Ignore air resistant, only gravitational acceleration g = -9.81 m/s2 affect the ball vertically. We can use the following equation to calculate the time it takes to reach maximum height (at 0 speed)
So the vertical distance it travels within time t is
Similarly the horizontal distance it travels within time t is:
We can pre-calcualte the quantity
So
From here we can plug-in the angles values of 30, 45 and 60 degrees
At 30 degrees, height = 14.39 m and distance = 49.83 m
At 45 degrees, height = 28.77 m and distance = 57.54 m
At 60 degrees, height = 43.16 m and distance = 49.83 m