Answer:
a) fr = 224.3 N
, b) fr = 224.3 N
, c) v = 198.0 m/s
Explanation:
a) For this exercise let's start by calculating the acceleration in the fall
v² = v₀² - 2 a (y-y₀)
When it jumps the initial vertical speed is zero
a = -v² / 2 (y-y₀)
a = -68 2/2 (1000-2000)
a = 2,312 m / s²
Let's use the second net law to enter the average friction force
fr = m a
fr = 97 2,312
fr = 224.3 N
b) let's look for acceleration
v² = v₀² - 2 a y
a = (v² –v₀²) / 2 (y-y₀)
a = (4² - 68²) / 2 (0-1000)
a = 2,304 m / s²
fr = m a
fr = 97 2,304
fr = 223.5 N
c) the speed of the wallet is searched with kinematics
v² = v₀² - 2 g (y-y₀)
v = √ (0-2 9.8 (0-2000))
v = 198.0 m/s
Answer:
5.4 ms⁻¹
Explanation:
Here we have to use conservation of energy. Initially when the stick is held vertical, its center of mass is at some height above the ground, hence the stick has some gravitational potential energy. As the stick is allowed to fall, its rotates about one. gravitational potential energy of the stick gets converted into rotational kinetic energy.
= length of the meter stick = 1 m
= mass of the meter stick
= angular speed of the meter stick as it hits the floor
= speed of the other end of the stick
we know that, linear speed and angular speed are related as
= height of center of mass of meter stick above the floor = 
= Moment of inertia of the stick about one end
For a stick, momentof inertia about one end has the formula as
Using conservation of energy
Rotational kinetic energy of the stick = gravitational potential energy
Acceleration = (final velocity^2 - initial velocity^2) / 2 * distance
Acceleration = (19.1^2 - 9.2^2) / 2 * 32
Acceleration = (364.81 - 84.64) / 64
Acceleration = 280.17 / 64
Acceleration = 4.3777m/s^2
:)
Answer:
(i) -556 rad/s²
(ii) 17900 revolutions
(iii) 11250 meters
(iv) -55.6 m/s²
(v) 18 seconds
Explanation:
(i) Angular acceleration is change in angular velocity over time.
α = (ω − ω₀) / t
α = (10000 − 15000) / 9
α ≈ -556 rad/s²
(ii) Constant acceleration equation:
θ = θ₀ + ω₀ t + ½ αt²
θ = 0 + (15000) (9) + ½ (-556) (9)²
θ = 112500 radians
θ ≈ 17900 revolutions
(iii) Linear displacement equals radius times angular displacement:
s = rθ
s = (0.100 m) (112500 radians)
s = 11250 meters
(iv) Linear acceleration equals radius times angular acceleration:
a = rα
a = (0.100 m) (-556 rad/s²)
a = -55.6 m/s²
(v) Angular acceleration is change in angular velocity over time.
α = (ω − ω₀) / t
-556 = (0 − 15000) / t
t = 27
t − 9 = 18 seconds
Answer:
The vector sum of all forces acting on it is zero, its at equilibrium.
Explanation:
The bag of marbles hanging on a spring scale applies its weight downwards, which was counterbalanced by the reaction from the spring scale (obeying the Newton's third law of motion). And since no external forces are applied to the system, thus the equilibrium of the system.
If the weight of the bag is greater than the reaction from the spring scale, the scale breaks and the system would not be balanced.
