Two Students are pulling on a box initially at rest with a mass of 13.5 kg on a frictionless surface. Student #1 is applying a force of 16.5 N to the left while student #2 is apply a force of 3.7 N to the right. Find the velocity of the box after 6 sec
net force=mass*a
16.5-3.7=(13.5) a
solve for a.
then,
vf=a*t
f=ma
16.5-3.7=<13.5*9.8m/s =-
To find the velocity of the box after 6 seconds, we can use Newton's Second Law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Step 1: Calculate the net force acting on the box.
The net force is the vector sum of the forces acting on the box. In this case, Student #1 is pulling to the left with a force of 16.5 N, and Student #2 is pulling to the right with a force of 3.7 N.
Net force = Force applied by Student #1 - Force applied by Student #2
Net force = 16.5 N - 3.7 N
Net force = 12.8 N
Step 2: Calculate the acceleration of the box.
We can use Newton's Second Law to find the acceleration.
Acceleration = Net force / Mass
Acceleration = 12.8 N / 13.5 kg
Acceleration ≈ 0.9481 m/s² (rounded to four decimal places)
Step 3: Calculate the velocity of the box after 6 seconds.
The velocity of an object can be calculated using the formula:
Velocity = Initial velocity + (Acceleration * Time)
Since the box is initially at rest, the initial velocity is 0 m/s.
Velocity = 0 + (0.9481 m/s² * 6 s)
Velocity ≈ 5.6886 m/s (rounded to four decimal places)
So, the velocity of the box after 6 seconds is approximately 5.6886 m/s.
To find the velocity of the box after 6 seconds, 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.
In this case, the net force acting on the box can be found by subtracting the force applied by Student #2 (3.7 N to the right) from the force applied by Student #1 (16.5 N to the left).
Net force = Force applied by Student #1 - Force applied by Student #2
= 16.5 N - 3.7 N
= 12.8 N to the left
Next, we can use the equation F = m * a, where F is the net force, m is the mass of the object, and a is the acceleration. Rearranging the equation to solve for acceleration, we have:
a = F / m
Plugging in the values, we get:
a = 12.8 N / 13.5 kg
≈ 0.948 m/s² to the left
Now we can use the equation v = u + a * t, where v is the final velocity, u is the initial velocity (which is 0 m/s since the box starts from rest), a is the acceleration, and t is the time. Rearranging the equation to solve for v, we have:
v = u + a * t
= 0 m/s + 0.948 m/s² * 6 s
≈ 5.688 m/s to the left
Therefore, the velocity of the box after 6 seconds is approximately 5.688 m/s to the left.