A mass of 8 kg lies on a horizontal, frictionless floor. A force of 53 Newtons pushes to the left (negative x direction) with a force of 53 Newtons. Another force of unknown magnitude pushes the mass in a direction of 28.5 degrees above the positive x axis. The mass is originally at rest before these forces are applied and 2.9 seconds after the forces have been applied, the mass has moved to the left a distance of 11.5 meters. What is the magnitude of the unknown force in Newtons?
V = 11.5m. / 2.9s. = 3.97m/s.
a = (Vf - Vo) / t,
a =(3.97 - 0) / 2.9 = 1.37m/s^2.
Fn = ma = 8 * 1.37 = 10.94N.
Fn = -57 + F*cos28.5 = 10.94,
-57 + 0.879F = 10.94,
0.879F = 10.94 + 57 = 67.94,
F = 77.3N
To find the magnitude of the unknown force, you can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. We can break down the forces acting on the mass:
1. The force pushing to the left (negative x direction) with a magnitude of 53 Newtons.
2. The unknown force acting at an angle of 28.5 degrees above the positive x-axis.
First, let's find the acceleration of the object. We can use the kinematic equation:
s = ut + (1/2)at^2
Where:
s = displacement (11.5 meters)
u = initial velocity (0 m/s since the mass is originally at rest)
t = time (2.9 seconds)
a = acceleration (unknown)
Rearranging the equation, we get:
a = 2s / t^2
a = 2 * 11.5 / (2.9)^2
a ≈ 7.97 m/s^2 (rounded to two decimal places)
Now we can calculate the net force acting on the object:
Net Force = mass * acceleration
Given that the mass is 8 kg:
Net Force = 8 kg * 7.97 m/s^2
Net Force ≈ 63.76 N (rounded to two decimal places)
Since the net force is the sum of the forces acting on the object, we can calculate the magnitude of the unknown force as follows:
Unknown Force + 53 N = 63.76 N
Therefore:
Unknown Force = 63.76 N - 53 N
Unknown Force ≈ 10.76 N (rounded to two decimal places)
Hence, the magnitude of the unknown force is approximately 10.76 Newtons.