A 2 kg block is pulled from rest along a horizontal surface by a rope with a force of 16 N. It experiences a constant frictional force of 3 N. How far has the block moved in the first five seconds?
The net force pulling the block is
F = 16 - 3 = 13 N
The acceleration rate is
a = F/m = 6.5 m/s^2
The distance moved in thime t is
X = (a/2)*t^2
Substitute t = 5 s and compute.
To determine how far the block has moved in the first five seconds, we need to apply Newton's second law of motion and use the equation of motion.
Newton's second law of motion states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F_net = m * a
In this case, the net force consists of the applied force and the force of friction:
F_net = F_applied - F_friction
Given:
- Mass of the block (m) = 2 kg
- Applied force (F_applied) = 16 N
- Force of friction (F_friction) = 3 N
Let's calculate the acceleration of the block using Newton's second law:
F_net = m * a
16 N - 3 N = 2 kg * a
13 N = 2 kg * a
Next, we need to find the acceleration (a) of the block:
a = 13 N / 2 kg
a = 6.5 m/s^2
Now that we have the acceleration, we can use the equation of motion to determine the distance traveled in the first five seconds:
d = v0 * t + (0.5 * a * t^2)
However, since the block is at rest initially, the initial velocity (v0) is zero. Therefore, the equation simplifies to:
d = 0.5 * a * t^2
where:
- d is the distance traveled
- a is the acceleration
- t is the time
Let's plug in the values:
d = 0.5 * 6.5 m/s^2 * (5 s)^2
d = 0.5 * 6.5 m/s^2 * 25 s^2
d = 0.5 * 6.5 m/s^2 * 625 s^2
d = 2031.25 m
Therefore, the block has moved a distance of 2031.25 meters in the first five seconds.