A large box whose mass is 19.0 kg rests on a frictionless floor. A mover pushes on the box with a force of 235 N at an angle 34.8° below the horizontal. Draw the box's free-body diagram and use it to determine the acceleration of the box. m/s2
Since the force 235 N is at an angle, you want it to be parallell with the ground. To do that you do the cosine of the angle multiplied by the force. So
235*cos34.8
=
192.97 N
Using F=ma
192.97=19a
so a= 10.1563 m/s^2
Well, well, well, looks like we have a physics problem on our hands! Let's see what we can do here.
First things first, let's draw that free-body diagram, shall we? Imagine a large box sitting on a frictionless floor. The only forces acting on the box are the force of gravity pulling it downwards and the force applied by the mover at an angle below the horizontal. Got the image in your head? Good! Now, let's move on.
Since the box is resting on a frictionless floor, the force of gravity and the normal force (the force exerted by the floor on the box) cancel each other out. So, we don't need to worry about those forces for now.
Now, the mover is pushing the box with a force of 235 N at an angle 34.8° below the horizontal. We can break this force down into its horizontal and vertical components. The horizontal component is given by 235 N * cos(34.8°), and the vertical component is given by 235 N * sin(34.8°). Are you with me so far? Great!
Now, here's a funny twist: since there is no friction to oppose the horizontal force, the only force that's actually going to make the box move is the horizontal component of the force applied by the mover. So, let's focus on that.
The horizontal component of the force is given by 235 N * cos(34.8°), which is approximately 194.3 N. This force, my friend, is the net force acting on the box.
Now, to determine the acceleration of the box, we can use Newton's second law, which states that the net force is equal to the mass of the object multiplied by its acceleration. Mathematically, it can be written as Fnet = m * a.
In this case, the net force is 194.3 N and the mass of the box is 19.0 kg. So, we can rearrange the equation to solve for the acceleration:
a = Fnet / m
= 194.3 N / 19.0 kg
≈ 10.2 m/s²
And there you have it! The acceleration of the box is approximately 10.2 m/s². I hope this answer brings a smile to your face, even if physics can sometimes be a bit of a circus!
To determine the acceleration of the box, we first need to draw the free-body diagram to identify the forces acting on it.
The forces acting on the box are:
1. Weight (mg) pointing downwards.
2. Normal force (N) exerted by the floor, pointing upwards.
3. Applied force (F) exerted by the mover at an angle of 34.8° below the horizontal.
Using trigonometry, we can break down the applied force into its horizontal and vertical components. The horizontal component (F_x) can be found using the equation: F_x = F * cos(θ), where θ is the angle of the force.
From the free-body diagram, we have:
1. Weight (mg) pointing downwards.
2. Normal force (N) exerted by the floor, pointing upwards.
3. Applied force component (F_x) pointing to the right.
4. Applied force component (F_y) pointing downwards.
Since the box is on a frictionless floor, there is no frictional force acting on it. Therefore, the normal force (N) is equal in magnitude and opposite in direction to the weight (mg).
Next, we use Newton's second law of motion, which states that the net force is equal to the mass of the object multiplied by its acceleration: ΣF = ma.
Considering the forces in the horizontal direction:
ΣF_x = F_x = ma, where a is the horizontal acceleration of the box.
Since the applied force is the only force acting on the box in the horizontal direction:
F_x = F * cos(θ)
Considering the forces in the vertical direction:
ΣF_y = N - mg = ma, where a is the vertical acceleration of the box.
Since the normal force (N) is equal in magnitude and opposite in direction to the weight (mg):
N = mg
Now we can find the values of the forces and the acceleration of the box.
Given:
Mass (m) = 19.0 kg
Applied force (F) = 235 N
Angle (θ) = 34.8°
Acceleration (a) = ?
Using the above equations, we can find:
F_x = F * cos(θ)
F_y = F * sin(θ)
N = mg
ΣF_x = F_x = ma
ΣF_y = N - mg = ma
First, we need to calculate the components of the applied force (F_x and F_y):
F_x = 235 N * cos(34.8°)
F_y = 235 N * sin(34.8°)
Next, we can find the normal force (N) using the formula:
N = mg
Now, we can substitute the values into the equations for acceleration:
ΣF_x = F_x = ma
ΣF_y = N - mg = ma
Finally, we can solve for the acceleration (a).
To determine the acceleration of the box, we need to draw the free-body diagram and analyze the forces acting on it. Here's how you can do it:
1. Draw a diagram representing the box as a rectangle.
2. Mark the direction of gravity downwards, which we can represent with the weight force (mg) acting at the center of the box vertically downward.
3. Now, let's focus on the force applied by the mover. This force is at an angle of 34.8° below the horizontal. To break it into its horizontal and vertical components, draw a horizontal line from the tip of the force vector and a vertical line from the tip to represent these components.
4. The horizontal component is the force pushing the box horizontally, and it is given by F(horizontal) = F * cos(θ), where F is the magnitude of the applied force and θ is the angle. In this case, F(horizontal) = 235 N * cos(34.8°).
5. The vertical component is responsible for counteracting the weight force and preventing the box from moving upward. It is given by F(vertical) = F * sin(θ), where F is the magnitude of the applied force and θ is the angle. In this case, F(vertical) = 235 N * sin(34.8°).
6. Now, let's analyze the forces. We have the weight force (mg) acting downward and the vertical component of the applied force (F(vertical)) acting upward. These two forces cancel each other out since the box is not moving vertically.
7. The only horizontal force is the applied force's horizontal component (F(horizontal)), which causes the acceleration of the box.
8. Now, we can use Newton's second law of motion, F = ma, where F is the net force, m is the mass of the box, and a is the acceleration. In this case, the net force is the horizontal component of the applied force (F(horizontal)), and the mass is given as 19.0 kg.
9. Plugging in the values, we get F(horizontal) = ma, so a = F(horizontal) / m.
Now, substitute the values and calculate the acceleration:
a = (235 N * cos(34.8°)) / 19.0 kg
Using a calculator, compute the value and express it in m/s^2.