A 8.5 kg block intially at rest is pulled to the rightr along a horizontal, frictionless surface by a constant horizontal force of 15.6 Newtons. Find the speed of the block after 2.8 meter
F=ma find a.
then vf^2=2ad
To find the speed of the block after it has traveled a distance of 2.8 meters, we need to use the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (speed)
u = initial velocity (which is zero, as the block was initially at rest)
a = acceleration
s = distance traveled
In this case, the force applied to the block is causing an acceleration. We can calculate the acceleration using Newton's second law, which states that the force applied to an object is equal to its mass multiplied by its acceleration:
F = ma
Given that the force exerted on the block is 15.6 Newtons and the mass of the block is 8.5 kg, we can rearrange the equation to solve for acceleration:
a = F/m = 15.6 N / 8.5 kg
We can now substitute the obtained value of acceleration into the equation of motion:
v^2 = 0 + 2 * a * s
v^2 = 2 * (15.6 N / 8.5 kg) * 2.8 m
v^2 = (2 * 15.6 * 2.8) / 8.5
v^2 = 8.32 m^2/s^2
Finally, taking the square root of both sides, we can find the speed of the block:
v = sqrt(8.32) m/s
v ≈ 2.88 m/s
Therefore, the speed of the block after traveling a distance of 2.8 meters is approximately 2.88 m/s.
To find the speed of the block after it has been pulled, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the acceleration of the block. The formula to calculate acceleration is:
acceleration = force / mass
In this case, the force applied is 15.6 Newtons, and the mass of the block is 8.5 kg.
acceleration = 15.6 N / 8.5 kg
acceleration ≈ 1.84 m/s^2
Now, let's calculate the final speed of the block. We can use the kinematic equation:
final velocity^2 = initial velocity^2 + 2 * acceleration * distance
Since the block starts at rest (initial velocity is 0), the equation simplifies to:
final velocity^2 = 2 * acceleration * distance
Plugging in the values, we have:
final velocity^2 = 2 * 1.84 m/s^2 * 2.8 m
final velocity^2 ≈ 10.304 m^2/s^2
To find the final velocity, we take the square root of both sides:
final velocity ≈ √(10.304 m^2/s^2)
final velocity ≈ 3.21 m/s
Therefore, the speed of the block after 2.8 meters is approximately 3.21 m/s.