Boxes A and B are connected to each end of a light vertical rope, as shown in the following figure. A constant upward force 90.0 N is applied to box A. Starting from rest, box B descends 10.0 m in 4.50 s. The tension in the rope connecting the two boxes is 34.0 N
What is the mass of box B
What is the mass of box A
To find the mass of box B, we can use Newton's second law of motion which states that the net force acting on an object is equal to the product of its mass and acceleration.
First, let's calculate the acceleration of box B using the information given. We know that box B descends a distance of 10.0 m in a time of 4.50 s.
To find the acceleration, we use the equation for uniform acceleration:
a = (Δv) / t,
where Δv is the change in velocity, and t is the time.
Since the box starts from rest, its initial velocity (vi) is 0 m/s, so the change in velocity is:
Δv = vf - vi
= vf - 0
= vf,
where vf is the final velocity.
Using the equation for distance traveled during uniform acceleration:
d = vi * t + (1/2) * a * t^2,
we can rewrite it as:
Δd = d - di,
= d - 0,
= d,
where Δd represents the change in distance traveled.
We can solve this equation for the final velocity:
vf = (2 * Δd) / t + vi
= (2 * 10.0 m) / 4.50 s + 0
= 4.44 m/s.
Now that we have the final velocity of box B, we can find its acceleration using the equation:
a = Δv / t
= (4.44 m/s - 0 m/s) / 4.50 s
= 0.98 m/s^2.
With the acceleration of box B determined, we can now use Newton's second law to find its mass:
F = m * a,
where F is the net force acting on the object, m is the mass, and a is the acceleration.
The net force in this case is the tension in the rope, which is given as 34.0 N.
34.0 N = m * 0.98 m/s^2.
Solving for m:
m = 34.0 N / 0.98 m/s^2
≈ 34.7 kg.
Therefore, the mass of box B is approximately 34.7 kg.
To find the mass of box A, we can use the same approach. However, since box A is being pushed upwards with a constant force of 90.0 N, we can also use Newton's second law to find its mass.
Using the equation:
F = m * a,
we can rewrite it as:
90.0 N = m * g,
where m is the mass of box A and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Solving for m:
m = 90.0 N / 9.8 m/s^2
≈ 9.18 kg.
Therefore, the mass of box A is approximately 9.18 kg.