A large box whose mass is 20 kg rests on a frinctionless floor. A mover pushes on the box with a force of 250 N at an angle of 35 degrees below the horizontal. What is the acceleration of the box across the floor?
250 cos 35 = horizontal force
a = F / m = (250 cos 35)/20
Well, let's see. We have a large box on a frictionless floor, and a mover is pushing it with a force of 250 N at an angle of 35 degrees below the horizontal. So, basically, the mover is giving the box a little nudge in a particular direction.
Now, since the floor is frictionless, the only force acting on the box is the force applied by the mover. We can break this force into two components: one parallel to the floor, and one perpendicular to the floor. The component parallel to the floor is the force that will accelerate the box.
To find this component, we need to do a little trigonometry. We can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. Rearranging the equation to solve for a, we get a = F/m.
Now, to find the component of the force parallel to the floor, we use the formula F_parallel = F * cos(theta), where theta is the angle the force makes with the horizontal. In this case, theta is 35 degrees below the horizontal, so we take the cosine of -35 degrees.
Plugging in the values, we get a = 250 N * cos(-35 degrees) / 20 kg. Using some trigonometric wizardry, we find that cos(-35 degrees) = cos(35 degrees) = 0.819, approximately.
So, the acceleration of the box across the floor is a = 250 N * 0.819 / 20 kg. Crunching those numbers, we get a ≈ 10.3 m/s².
Voila! The box will accelerate across the floor at a rate of approximately 10.3 meters per second squared. Now just be careful not to slip and slide yourself while you're pushing it!
To find the acceleration of the box, we can use Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, we need to resolve the force into its horizontal and vertical components. The vertical component does not affect the motion along the floor, so we only need to consider the horizontal component.
The horizontal component of the force can be found by using the cosine of the angle between the force vector and the horizontal axis:
Horizontal component of the force = Force × cos(angle)
Then, we can use Newton's second law to find the acceleration:
Acceleration = Net horizontal force / mass
Let's calculate the horizontal component of the force first:
Horizontal component of the force = 250 N × cos(35°)
Horizontal component of the force ≈ 250 N × 0.819
Horizontal component of the force ≈ 204.75 N
Now, we can calculate the acceleration:
Acceleration = Net horizontal force / mass
Acceleration = 204.75 N / 20 kg
Acceleration ≈ 10.24 m/s²
Therefore, the acceleration of the box across the floor is approximately 10.24 m/s².
To find the acceleration of the box across the floor, we can use 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.
Step 1: Resolve the force into its horizontal and vertical components.
The force applied by the mover can be resolved into its horizontal and vertical components using trigonometry. The horizontal component (F_horizontal) can be calculated using the equation:
F_horizontal = F * cos(theta), where F is the magnitude of the force (250 N) and theta is the angle of 35 degrees.
F_horizontal = 250 N * cos(35 degrees)
F_horizontal = 250 N * 0.819
F_horizontal ≈ 204.75 N
The vertical component (F_vertical) can be calculated using the equation:
F_vertical = F * sin(theta), where F is the magnitude of the force (250 N) and theta is the angle of 35 degrees.
F_vertical = 250 N * sin(35 degrees)
F_vertical = 250 N * 0.574
F_vertical ≈ 143.5 N
Step 2: Determine the net force acting on the box.
Since there is no friction between the box and the floor, the only force acting on the box is the horizontal component of the applied force.
Net force = F_horizontal
Net force = 204.75 N
Step 3: Calculate the acceleration of the box.
Now that we know the net force acting on the box, we can use Newton's second law to calculate the acceleration. The formula is:
Net force = mass of the box * acceleration
Since the mass of the box is given as 20 kg, we can rearrange the formula to solve for acceleration:
acceleration = Net force / mass
acceleration = 204.75 N / 20 kg
acceleration ≈ 10.24 m/s²
Therefore, the acceleration of the box across the floor is approximately 10.24 m/s².