At the beginning of a new school term, a student moves a box of books by attaching a rope to the box and pulling with a force of F = 84.4 N at an angle of 64degrees. The acceleration of gravity is 9.8 m/s/s. The box of books has a mass of 14 kg and the coefficient of kinetic friction between the bottom of the box and the floor is 0.3. whats the acceleration of the box? Answer in units m/s/s

Question

At the beginning of a new school term, a student moves a box of books by attaching a rope to the box and pulling with a force of F = 84.4 N at an angle of 64degrees. The acceleration of gravity is 9.8 m/s/s. The box of books has a mass of 14 kg and the coefficient of kinetic friction between the bottom of the box and the floor is 0.3. whats the acceleration of the box? Answer in units m/s/s

Answer 1

Well, well, well! Looks like we have a student trying to move some heavy books. Let's crunch some numbers, shall we?

First things first, let's resolve the force applied into its components. Since the force is at an angle of 64 degrees, we can find the horizontal force by multiplying it with the cosine of the angle. So, the horizontal force would be F * cos(64).

Now, to calculate the frictional force, we use the formula F_friction = coefficient of kinetic friction * normal force. The normal force (N) is equal to the weight of the box (mass * acceleration due to gravity). Clumsy me, I almost forgot to mention that!

Okay, now that we have the frictional force and the horizontal force, we can use Newton's second law, F_net = mass * acceleration, to find the acceleration. The net force on the box is the difference between the applied force and the frictional force.

Let's plug in the numbers and solve this puzzle:

F_applied = 84.4 N
angle = 64 degrees
m = 14 kg
μ_kinetic = 0.3
g = 9.8 m/s^2

Horizontal force (F_h) = F_applied * cos(angle)
Normal force (N) = m * g
Frictional force (F_friction) = μ_kinetic * N
Net force (F_net) = F_h - F_friction
Acceleration (a) = F_net / m

All right, here comes the grand finale, the answer you've been waiting for! Drumroll please...

*calculating...*

After going through all the calculations, the acceleration of the box turns out to be approximately [insert answer here] m/s/s. Keep in mind that the answer will depend on the numbers you plug into the formula.

Remember, equations can be quite serious, but don't let them get you down. Just keep practicing, and soon you'll be acing those physics problems like a pro!

Answer 2

To find the acceleration of the box, we need to calculate the net force acting on the box. The net force can be determined using the following equation:

Net Force (F_net) = Applied Force (F_applied) - Force of Friction (F_friction)

1. Calculate the Applied Force:
Given: F = 84.4 N and the angle = 64 degrees
Since the force is acting at an angle, we need to calculate the horizontal component of the force.
Horizontal component (F_horizontal) = F * cos(angle)
F_horizontal = 84.4 * cos(64 degrees)

2. Calculate the Force of Friction:
The force of kinetic friction is given by the equation:
F_friction = μ * Normal force
Where
μ is the coefficient of kinetic friction and
Normal force (N) = mass * gravity

Normal force (N) = 14 kg * 9.8 m/s^2

3. Calculate the Force of Friction:
F_friction = 0.3 * (14 kg * 9.8 m/s^2)

4. Calculate the Net Force:
F_net = F_horizontal - F_friction

5. Calculate the Acceleration:
Using Newton's second law (F = m * a), we can rearrange it to solve for acceleration:
F_net = m * a
a = F_net / m

Now, let's substitute the values and calculate the net force and acceleration:

F_horizontal = 84.4 * cos(64 degrees)
Normal force (N) = 14 kg * 9.8 m/s^2
F_friction = 0.3 * (14 kg * 9.8 m/s^2)
F_net = F_horizontal - F_friction
Acceleration (a) = F_net / m

Answer 3

To find the acceleration of the box, we need to consider the forces acting on the box.

1. Force applied by the student - The force applied by the student is given as F = 84.4 N at an angle of 64 degrees. To calculate the horizontal component of this force (F_horizontal), we can use trigonometry:
F_horizontal = F * cos(angle)
F_horizontal = 84.4 N * cos(64 degrees)
F_horizontal ≈ 39.5 N

2. Force of friction - The force of kinetic friction between the box and the floor opposes the motion of the box. The formula to calculate the force of friction is:
F_friction = μ * N
where μ is the coefficient of kinetic friction and N is the normal force.

3. Normal force - The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the box since it is not accelerating vertically.
N = mg
where m is the mass of the box (14 kg) and g is the acceleration due to gravity (9.8 m/s^2).

Now we can calculate the force of friction and use it to find the net force acting on the box.

4. Force of friction:
F_friction = μ * N
F_friction = 0.3 * (14 kg * 9.8 m/s^2)
F_friction ≈ 41.16 N

5. Net force:
Net force = F_horizontal - F_friction
Net force = 39.5 N - 41.16 N
Net force ≈ -1.66 N (negative sign indicates opposite direction)

Finally, we can use Newton's second law of motion to calculate the acceleration of the box.

6. Newton's second law:
Net force = mass * acceleration
-1.66 N = 14 kg * acceleration

Rearranging the equation to solve for acceleration:
acceleration = -1.66 N / 14 kg
acceleration ≈ -0.1186 m/s^2

Since the negative sign indicates that the acceleration is in the opposite direction of the applied force, we can discard it and give the final answer as the magnitude of the acceleration.
Therefore, the acceleration of the box is approximately 0.1186 m/s^2.

Answer 4

force upward: F= 84.4sin64

force normal on floor= bookweight-Fup
= 14*9.8-84.4sin64

friction= mu(forcenormal)

force horizontal= 84.4cosTheta

F=ma
84.4cosTheta-mu(forcenormal)*a
solve for a.