Answer:
3.46 seconds
Explanation:
Since the ball is moving in circular motion thus centripetal force will be acting there along the rope.
The equation for the centripetal force is as follows -
Where, 
is the mass of the ball, 
is the speed and 
is the radius of the circular path which will be equal to the length of the rope.
This centripetal force will be equal to the tension in the string and thus we can write,
and, 
Thus, 
m/s.
Now, the total length of circular path = circumference of the circle
Thus, total path length = 2πr = 2 × 3.14 × 2 = 12.56 m
Time taken to complete one revolution = 
= 
= 3.46 seconds.
Thus, the mass will complete one revolution in 3.46 seconds.
We are given the gravitational potential energy and the height of the ball and is asked in the problem to determine the mass of the ball. the formula to be followed is PE = mgh where g is the gravitational acceleration equal to 9.81 m/s^2. substituting, 58.8 J = m*9.8 m/s^2 * 30 m; m = 0.2 kg.
Answer:
143 batteries does Benny need to sample
Explanation:
Given data
confidence level = 97%
error = ±10 hours
standard deviation SD = 55 hours
to find out
how many batteries does Benny need to sample
solution
confidence level is 97%
so a will be 1 - 0.97 = 0.03
the value of Z will be for a 0.03 is 2.17 from standard table
so now we calculate no of sample i.e
no of sample = (Z× SD/ error)²
no of sample = (2.16 × 55 / 10)²
no of sample = 142.44
so 143 batteries does Benny need to sample
Answer:
-54 m/s²
Explanation:
Acceleration is defined as the change in velocity of a body with respect to time. Mathematically,
Acceleration A = change in velocity/time
A = dv/dt
Given Vx = at − bt³
The time at which the particle reaches its maximum displacement is at when vx = 0.
0 = at-bt³
t(a-bt²) = 0
a-bt² = 0
a = bt²
t² = a/b ... (1)
A = dvx/dt = a - 3bt²(by differentiating)
Acceleration = a - 3bt²... (2)
Substituting t² = a/b into equation 2 will give;
Acceleration = a - 3b(a/b)
Acceleration = a-3a
Acceleration = -2a
Substituting the value of a = 27m/s into the resulting equation of acceleration gives;
Acceleration = -2(27)
Acceleration = -54m/s²
Therefore at maximum displacement in the positive x direction, the acceleration of the particle will be -54m/s²
