Answer:
The smallest angular velocity is 4.42 rad/s and the largest angular velocity is 13.15 rad/s for the toast to hit and then topple to be butter-side down
Explanation:
62 cm = 0.62 m
Knowing that the vertical distance traveled is s = 0.62 m and gravitational acceleration is g = 9.81 m/s2, we can calculate the time of falling
If there's only 0.36s to rotate, and for the toast to hit and then topple to be butter-side down, then the angle of rotation must be between 90 and 270 degrees (Suppose that it starts with butter up and it rotates less than 1 revolution, or 360 degrees):
In other words (and units):
rad
As :
rad/s
rad/s
rad/s
So the smallest angular velocity is 4.42 rad/s and the largest angular velocity is 13.15 rad/s for the toast to hit and then topple to be butter-side down
Answer:
(a) 34.4°
(b) 49.4 N
Explanation:
(a) From the diagram,
Amgle between the x axis can be calculated as,
cosΘ = adjacent/hypoteneous
cosΘ = 72.1/87.4
cosΘ = 0.8249
Θ = cos⁻¹(0.8249)
Θ = 34.4°.
Hence the angle between the x axis is 34.4°
(b) To find the component along the y axis we make use of pythagoras theorem.
a² = b²+c²................... Equation 1
Where a = 87.4 N, b = 72.1 N, c = y.
Substitute these values into equation 1
87.4² = 72.1² + y²
y² = 87.4²-72.1²
y² = 2440.35
y = √(2440.35)
y = 49.4 N
