A force F=160N is applied to the cord. Determine how high the 400N block A rises in 2s starting from rest . Neglect the weigth of the pulleys and cord.
To determine how high the 400N block A rises in 2 seconds, we need to understand the concept of work and energy.
First, let's calculate the work done on block A. The work done is equal to the force applied multiplied by the distance over which the force is applied. In this case, since the force is being applied vertically, the distance will be the height the block A rises.
Work (W) = Force (F) × Distance (d)
We know that the force applied is 160N, but we need to find the distance. To find the distance, we can use the equation of motion for uniformly accelerated motion:
d = ut + (1/2)at^2
Where:
d = distance
u = initial velocity (since the block starts from rest, u = 0)
t = time (given as 2s)
a = acceleration (which we will determine)
To find the acceleration, we can use Newton's second law:
Force (F) = mass (m) × acceleration (a)
We're given that the weight of block A is 400N. Weight (W) is equal to mass (m) × acceleration due to gravity (g).
Weight (W) = m × g
Since we neglect the weight of the pulleys and cord, the weight of the block A is equal to the force applied (F).
F = m × g
We can rearrange this equation to find the acceleration (a):
a = F / m
Now we have all the necessary values to calculate the distance (d) using the equation of motion:
d = (1/2) × a × t^2
Now let's put all the values into their respective equations and calculate the distance.
1. Calculate the acceleration:
a = F / m = 160N / 400kg = 0.4 m/s^2
2. Calculate the distance:
d = (1/2) × a × t^2 = (1/2) × 0.4 m/s^2 × (2s)^2 = 0.8 meters
Therefore, the 400N block A rises to a height of 0.8 meters in 2 seconds, starting from rest.