a) The kinetic energy (KE) of an object is expressed as the product of half of the mass (m) of the object and the square of its velocity (v²):
It is given:
v = 8.5 m/s
m = 91 kg
So:
b) We can calculate height by using the formula for potential energy (PE):
PE = m*g*h
In this case, h is eight, and PE is the same as KE:
PE = KE = 3,287.4 J
m = 91 kg
g = 9.81 m/s² - gravitational acceleration
h = ? - height
Now, let's replace those:
3,287.4= 91 * 9.81 * h
⇒ h = 3,287.4/(91*9.81) = 3,287.4/892.7 = 3.7 m
Answer:
-0.0789 m
Explanation:
Recall that the y-component comes associated with the sin(18.4) through the following trigonometric relationship:
y = 0.250 sin(-18.4) ≈ -0.0789 m
Notice it is negative since it is below the x-axis.
Answer:
The angular acceleration of the pencil<em> α = 17 rad·s⁻²</em>
Explanation:
Using Newton's second angular law or torque to find angular acceleration, we get the following expressions:
τ = I α (1)
W r = I α (2)
The weight is that the pencil has is,
sin 10 = r / (L/2)
r = L/2(sin(10))
The shape of the pencil can be approximated to be a cylinder that rotates on one end and therefore its moment of inertia will be:
I = 1/3 M L²
Thus,
mg(L / 2)sin(10) = (1/3 m L²)(α)
α(f) = 3/2(g) / Lsin(10)
α = 3/2(9.8) / 0.150sin(10)
<em> α = 17 rad·s⁻²</em>
Therefore, the angular acceleration of the pencil<em> </em>is<em> 17 rad·s⁻²</em>
Monoammonium phosphate effectively smothers the fire, while sodium bicarbonate induces a chemical reaction which extinguishes the fire. Fire extinguishers with a Class C rating are suitable for fires in “live” electrical equipment.
Answer:
Explanation:
Remark
At the time it takes to drop 20 m is the same time it takes to travel 60 m horizontally.
Givens
h = 20 m
hd = 60 m
g = 9.81
vi = 0
Formula
d = vi*t + 1/2 a * t^2 We are solving for t
Solution
When the battery fails, the vertical initial velocity is 0. So we have to find the time it would take to drop 20 meters
d = 0*t + 1/2 * 9.81 a* t^2
20 = 4.91 * t^2 Divide by 4.91
20/4.91 = 4.91 t^2 / 4.91
4.073 = t^2 Take the square root of both sides.
t = 2.02 seconds
Horizontal
d = 60 m
t = 2.02 seconds
v = ?
Note: there is no horizontal deceleration or acceleration
v = d/t
v = 60/2.02
Answer: v = 29.73 m/s
