There are many ways to solve this but I prefer to use the energy method. Calculate the potential energy using the point then from Potential Energy convert to Kinetic Energy at each points.
PE = KE
From the given points (h1 = 45, h2 = 16, h<span>3 </span>= 26)
Let’s use the formula:
v2= sqrt[2*Gravity*h1] where the gravity is equal to 9.81m/s2
v3= sqrt[2*Gravity*(h1 - h3 )] where the gravity is equal to 9.81m/s2
v4= sqrt[2*Gravity*(h1 – h2)] where the gravity is equal to 9.81m/s2
Solve for v2
v2= sqrt[2*Gravity*h1]
= √2*9.81m/s2*45m
v2= 29.71m/s
v3= sqrt[2*Gravity*(h1 - h3 )
=√2*9.81m/s2*(45-26)
=√2*9.81m/s2*19
v3=19.31m/s
v4= sqrt[2*Gravity*(h1 – h2)]
=√2*9.81m/s2*(45-16)
=√2*9.81m/s2*(29)
v4=23.85m/s
Answer:
a. 0.21 rad/s2
b. 2.205 N
Explanation:
We convert from rpm to rad/s knowing that each revolution has 2π radians and each minute is 60 seconds
200 rpm = 200 * 2π / 60 = 21 rad/s
180 rpm = 180 * 2π / 60 = 18.85 rad/s
r = d/2 = 30cm / 2 = 15 cm = 0.15 m
a)So if the angular speed decreases steadily (at a constant rate) from 21 rad/s to 18.85 rad/s within 10s then the angular acceleration is
b) Assume the grind stone is a solid disk, its moment of inertia is
Where m = 28 kg is the disk mass and R = 0.15 m is the radius of the disk.
So the friction torque is
The friction force is
Since the friction coefficient is 0.2, we can calculate the normal force that is used to press the knife against the stone
What a delightful little problem !
-- When he is running on level ground, his kinetic energy is
KE = (1/2) x (mass) x (speed)² .
-- When he climbs up from the ground, his potential energy is
PE = (mass) x (gravity) x (height above the ground).
We're looking for the height that makes these quantities of energy equal,
figuring that when he runs, his speed is 11 m/s.
The first time I looked at this, I thought we would need to know the runner's
mass. But it turns out that we don't.
<u>PE = KE</u>
(mass) x (gravity) x (height) = (1/2) (mass) (11 m/s)²
Divide each side by (mass) :
(gravity) x (Height) = (1/2) (11 m/s)²
Divide each side by gravity:
Height = (1/2) (121 m²/s²) / (9.8 m/s²)
= <em>6.173 meters</em>
(about 20.3 feet !)