Answer:
The period of motion of new mass T = 0.637 sec
Explanation:
Given data
Mass of object (m) = 9 gm = 0.009 kg
Δx = 3.5 cm = 0.035 m
We know that spring force is given by
F = m g
F = 0.009 × 9.81 = 0.08829 N
Spring constant
k = 2.522
New mass = 26 gm = 0.026 kg
Now the period of motion is given by
T = 0.637 sec
This is the period of motion of new mass.
Answer:
Explanation:
If we make an analysis of the net force of the rock that was thrown upwards, we will have the following:
(1)
Where:
is the force with which the rock was thrown
is the weight of the rock
Being the weight the relation between the mass of the rock and the acceleration due gravity :
(2)
(3)
Substituting (3) in (1):
(4)
(5) This is the net Force on the rock
On the other hand, we know this force is equal to the multiplication of the mass with the acceleration, according to Newton's 2nd Law:
(6)
Finding the acceleration :
(7)
(8)
Finally:
Answer:
The spring force constant is .
Explanation:
We are told the mass of the ball is , the height above the spring where the ball is dropped is , the length the ball compresses the spring is and the acceleration of gravity is .
We will consider the initial moment to be when the ball is dropped and the final moment to be when the ball stops, compressing the spring. We supose that there is no friction so the initial mechanical energy is equal to the final mechanical energy :
Initially there is only gravitational potential energy because the force of the spring isn't present and the speed is zero. In the final moment there is only elastic potential energy because the height is zero and the ball has stopped. So we have that:
If we manipulate the equation we have that:
Answer:
5. -24 m/s²
Explanation:
Acceleration: This can be defined as the rate of change of velocity.
The S.I unit of acceleration is m/s².
mathematically,
a = dv/dt ............................ Equation 1
Where a = acceleration, dv/dt = is the differentiation of velocity with respect to time.
But
v = dx(t)/dt
Where,
x(t) = 27t-4.0t³...................... Equation 2
Therefore, differentiating equation 2 with respect to time.
v = dx(t)/dt = 27-12t²............. Equation 3.
Also differentiating equation 3 with respect to time,
a = dv/dt = -24t
a = -24t .................... Equation 4
from the question,
At the end of 1.0 s,
a = -24(1)
a = -24 m/s².
Thus the acceleration = -24 m/s²
The right option is 5. -24 m/s²
No. of protons = atomic number = 64
no. of neutrons = mass no. - no. of protons= 154 -64 = 90
no. of electrons = no. of protons = 64