Answer:
The amplitude of the subsequent oscillations is 13.3 cm
Explanation:
Given;
mass of the block, m = 1.25 kg
spring constant, k = 17 N/m
speed of the block, v = 49 cm/s = 0.49 m/s
To determine the amplitude of the oscillation.
Apply the principle of conservation of energy;
maximum kinetic energy of the stone when hit = maximum potential energy of spring when displaced
Therefore, the amplitude of the subsequent oscillations is 13.3 cm
Answer:
a) m₁ = m₂ F₁ₓ = F₂ₓ
b) m₁ << m₂ F₂ₓ =0
Explanation:
This interesting exercise is unclear your statement, so that in a center of mass system has an acceleration of zero it is necessary that the sum of the forces on each axis is zero, to see this we write Newton's second law
∑ F = m a
for acceleration to be zero implies that the net force is zero.
we must write the expression for the center of mass
= 1 / M (m₁ x₁ + m₂ x₂)
now let's use the derivatives
= d² x_{cm}/dt² = 1 / M (m₁ a₁ + m₂a₂)
where M is the total mass M = m₁ + m₂
so that the acceleration of the center of mass is zero
0 = 1 / M (m₁ a₁ + m₂a₂)
m₁ a₁ = - m₂ a₂
In the case that we have components on the x axis, the modulus of the two forces are equal and their direction is opposite, therefore
F₁ₓ = -F₂ₓ
b)r when the two masses are equal , in the case of a mass greater than the other m₁ << m₂
acm = d2 xcm / dt2 = 1 / M (m1 a1 + m2a2)
so that the acceleration of the center of mass is zero
0 = 1 / M (m1 a1 + m2a2)
m1 a1 = - m 2 a2
with the initial condition, we can despise m₁, therefore
0 = m₂a₂
if we use Newton's second law
F₂ = 0
I tell you that in this case with a very high mass difference the force on the largest mass must be almost zero
speed of the car is given on the road
reaction time is given as
now we can find the distance that it will move during this reaction time
now the deceleration of the car is 10 m/s^2
so the distance that it will move before stop is given by
so the total distance that it require to stop is given as
while the deer is standing at distance 38 m
so the car will stop 2.8 m before the position of deer
The characteristics of the projectile launch allows to find the results for the questions about the movement of the ball are:
Kinematics studies the motion of bodies looking for relationships between position, velocity and acceleration. In the case of vertical and projectiles launch the acceleration on the vertical axis is the acceleration of gravity directed downward.
In the attachment we can see the position of the ball for two distances in the case of projectile launching.
We can see that the speed of the ball decreases with height according to the relation
y = go t - ½ g t²
Where y is the height, g is the initial vertical velocity, g is the acceleration of gravity and t is time.
In all movements in various dimensions we assume that each movement in an . axis is independent
In the case of projectile launching, on the vertical axis there is an acceleration of gravity and on the horizontal axis there is no acceleration, the only parameter that this gives the two movements is the time, which is a scalar.
In conclusion, using the characteristics of the projectile launch, we can find the results for the questions about the movement of the ball are:
Learn more about projectile launch here: brainly.com/question/24888457
