The above free body diagram, the forces are acting on a 9.00 kg object. The x-axis is tilted up from the horizontal by 19.5 degrees. The magnitudes of the three forces are given by:
Force F1: 60.0 N
Force F2: 41.0 N
Force F3: 85.0 N.
What is the magnitude of the acceleration of the object?
The above free body diagram, the forces are acting on a 8.00 kg object. The x-axis is tilted down from the horizontal by 23.5 degrees. The magnitudes of the three forces are given by:
Force F1: 53.0 N
Force F2: 36.0 N
Force F3: 30.0 N.
What is the magnitude of the acceleration of the object?
To find the magnitude of the acceleration of the object, we first need to resolve the forces into their x-axis and y-axis components.
From the given information, we know that the x-axis is tilted up from the horizontal by 19.5 degrees. Let's call the angle between the x-axis and Force F1 as θ1, the angle between the x-axis and Force F2 as θ2, and the angle between the x-axis and Force F3 as θ3.
θ1 = 19.5 degrees (angle between x-axis and F1)
θ2 = 90 degrees (since F2 is perpendicular to the x-axis)
θ3 = 90 degrees (since F3 is perpendicular to the x-axis)
To find the x-axis component of each force (Fx), we use the equation: Fx = F * cos(θ), where F is the magnitude of the force and θ is the angle between the force and the x-axis.
For Force F1:
Fx1 = 60.0 N * cos(19.5 degrees)
For Force F2:
Fx2 = 41.0 N * cos(90 degrees) (cos(90 degrees) = 0)
For Force F3:
Fx3 = 85.0 N * cos(90 degrees) (cos(90 degrees) = 0)
Now let's find the net force in the x-axis direction (ΣFx) by summing up the x-axis components of all forces:
ΣFx = Fx1 + Fx2 + Fx3
Since Fx2 and Fx3 are both equal to zero, the net force in the x-axis direction becomes:
ΣFx = Fx1 + 0 + 0
Next, we can calculate the acceleration of the object using Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
ΣFx = m * ax,
where m is the mass of the object and ax is the acceleration in the x-axis direction.
So, we have:
ΣFx = m * ax
Now we can solve for the acceleration:
ax = ΣFx / m
Plugging in the values we have:
ax = (Fx1 + 0 + 0) / 9.00 kg
Finally, calculate the value of ax to find the magnitude of the acceleration.