A mass of 8 kg lies on a horizontal, frictionless floor. A force of 72 Newtons pushes to the left (negative x direction) with a force of 72 Newtons. Another force of unknown magnitude pushes the mass in a direction of 21.4 degrees above the positive x axis. The mass is originally at rest before these forces are applied and 2.4 seconds after the forces have been applied, the mass has moved to the left a distance of 11.1 meters. What is the magnitude of the unknown force in Newtons?
Please help me solve this problem =/
your use of the word "above"...is it operating against gravity, or is it still on the horizontal perpendicular to the x direction?
No it is not Operating against gravity. It is still on the horizontal
Keleigh are you a tutor?
at Bobpursley: No it's not Operating against gravity. It's still on the horizontal perpendicular to the x-direction.
To solve this problem, we need to 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.
First, let's find the acceleration of the mass using the information given. We can use the equation:
Net force = mass x acceleration
We know that the net force is the vector sum of the two forces applied to the mass:
Net force = -72 N (left) + unknown force
We can express the unknown force in terms of its x and y components using trigonometry:
unknown force = unknown force_x + unknown force_y
From the given angle of 21.4 degrees above the positive x-axis, we can find the x and y components of the unknown force as follows:
unknown force_x = unknown force * cos(21.4 degrees)
unknown force_y = unknown force * sin(21.4 degrees)
Now, substituting these components into the net force equation:
Net force_x = -72 N + unknown force_x
Net force_y = 0 N + unknown force_y
Next, we can find the acceleration in the x-direction using the equation:
Net force_x = mass * acceleration_x
Since the mass is 8 kg, we have:
-72 N + unknown force_x = 8 kg * acceleration_x
Now, let's consider the motion of the object in the x-direction. The displacement (distance moved) can be expressed as:
Displacement = initial velocity * time + 0.5 * acceleration_x * (time)^2
We are given that the mass originally at rest, so the initial velocity is zero. The time is given as 2.4 seconds, and the displacement is 11.1 meters to the left.
Plugging in these values:
11.1 m = 0 * 2.4 s + 0.5 * acceleration_x * (2.4 s)^2
Simplifying this equation, we can solve for the acceleration in the x-direction:
acceleration_x = (2 * 11.1 m) / (2.4 s)^2
Now, substitute this value of acceleration_x back into the net force equation:
-72 N + unknown force_x = 8 kg * (2 * 11.1 m) / (2.4 s)^2
Finally, solve for unknown force_x:
unknown force_x = 72 N + 8 kg * (2 * 11.1 m) / (2.4 s)^2
Using the value of unknown force_x, we can find the magnitude of the unknown force using the equation:
Unknown force = √(unknown force_x^2 + unknown force_y^2)
By substituting the values of unknown force_x and unknown force_y into this equation, you can calculate the magnitude of the unknown force.