A 200.0 N force moves a 120.0 kg crate on a friction less surface from rest to final speed of 9.6 m/s. what is the displacement of the crate at the time it reaches this speed ?
a = F/m = 200/120 = 1.67 m/s^2.
V^2 = Vo^2 + 2a*d.
d = (V^2-Vo^2)/2a
d = (92.16-0)/3.34 = 27.6 m.
Well, well, well, time to calculate some displacement! Let's get into the circus mood!
To calculate displacement, we need to know the acceleration of the crate. We can find that using good ol' Newton's second law. Since there is no friction, the only force acting on the crate is the applied force of 200.0 N.
Using Newton's second law (F = ma), we can rearrange it to find acceleration (a = F/m). For this scenario, the acceleration will be 200.0 N divided by the mass of the crate, which is 120.0 kg.
So, a = 200.0 N / 120.0 kg = 1.67 m/s² (rounded)
Now, we can use an equation of motion: v² = u² + 2as. In this equation:
v is the final velocity (9.6 m/s),
u is the initial velocity (0 m/s since the crate starts from rest),
a is the acceleration (1.67 m/s²),
and s is the displacement we want to find.
Plugging in the values, we get:
(9.6 m/s)² = (0 m/s)² + 2 * (1.67 m/s²) * s
Simplifying:
92.16 m²/s² = 3.34 m/s² * s
Now, let's isolate s (displacement):
s = 92.16 m²/s² / (3.34 m/s²)
Calculating this, we get:
s ≈ 27.6 meters (rounded)
So, the displacement of the crate when it reaches a speed of 9.6 m/s is approximately 27.6 meters.
Now, isn't that just a barrel of laughs? Enjoy your physics circus act!
To find the displacement of the crate, we can use the equation:
displacement = (final velocity² - initial velocity²) / (2 * acceleration)
In this case, the initial velocity is 0 m/s because the crate starts from rest, the final velocity is 9.6 m/s, and the acceleration can be found using Newton's second law:
force = mass * acceleration
Rearranging the equation, we can solve for acceleration:
acceleration = force / mass
Given that the force is 200.0 N and the mass is 120.0 kg, we can calculate the acceleration:
acceleration = 200.0 N / 120.0 kg
Now we can use the formula for displacement:
displacement = (9.6 m/s)² - (0 m/s)² / (2 * acceleration)
Calculating the acceleration:
acceleration = 200.0 N / 120.0 kg = 1.67 m/s²
Now we can substitute the values into the formula:
displacement = (9.6 m/s)² - (0 m/s)² / (2 * 1.67 m/s²)
Simplifying the equation:
displacement = 92.16 m²/s² / 3.34 m/s²
Finally, calculating the displacement:
displacement = 27.59 m
Therefore, the displacement of the crate at the time it reaches a speed of 9.6 m/s is 27.59 meters.
To find the displacement of the crate, we can use the equation:
Displacement = ((Final velocity)^2 - (Initial velocity)^2) / (2 * acceleration)
In this case, since the crate starts from rest and moves on a frictionless surface, the initial velocity is 0 m/s and there is no acceleration.
Therefore, the equation simplifies to:
Displacement = (Final velocity)^2 / (2 * acceleration)
To find the acceleration, we can use Newton's second law of motion:
Force = mass * acceleration
Given that the force acting on the crate is 200 N and the mass of the crate is 120 kg, we can rearrange the equation to solve for the acceleration:
acceleration = Force / mass
Substituting the values, we have:
acceleration = 200 N / 120 kg = 5/3 m/s^2
Now we can substitute the values of the final velocity and acceleration into the equation for displacement:
Displacement = (9.6 m/s)^2 / (2 * 5/3 m/s^2)
Simplifying,
Displacement = 92.16 m^2/s^2 / (10/3)
Dividing the numerator by the denominator,
Displacement = 92.16 m^2/s^2 * 3/10
Displacement = 27.648 m^2/s^2
Finally, taking the square root,
Displacement ≈ 5.26 m (rounded to two decimal places)
Therefore, the displacement of the crate at the time it reaches a final speed of 9.6 m/s is approximately 5.26 meters.