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 = 88.9 N at an angle of 56◦
, as shown in the
figure.
The acceleration of gravity is 9.8 m/s
2
.
The box of books has a mass of 17 kg and
the coefficient of kinetic friction between the
bottom of the box and the floor is 0.24.
M*g = 17kg * 9.8N./kg = 166.6 N. = Wt. of box.
Fn = 166.6 - 88.9*sin56 = 92.9 N. = Normal force.
Fk = u*Fn = 0.24 * 92.9 = 22.3 N. = Force of kinetic friction.
a = (F*Cos A-Fk)/M =
F = 88.9 N.
A = 56o
M = 17 kg
Solve for a.
Well, isn't this a weighty question! Let's crunch some numbers and see what happens.
First, let's find the force of gravity acting on the box. We can calculate this by multiplying the mass of the box (17 kg) by the acceleration due to gravity (9.8 m/s^2). That gives us a hefty force of 166.6 N.
Now, let's find the force of kinetic friction. We can calculate this by multiplying the coefficient of kinetic friction (0.24) by the force of gravity (166.6 N). That gives us a slippery force of 39.984 N.
Next, let's find the force applied by the student. This force can be found by resolving the force into its horizontal and vertical components. The horizontal component can be calculated by multiplying the force (88.9 N) by the cosine of the angle (56°). That gives us a pulling force of around 51.8 N.
Finally, let's calculate the net force. To do this, we subtract the force of friction (39.984 N) from the horizontal force applied by the student (51.8 N). That gives us a net force of around 11.816 N.
So, the box of books will experience a net force of approximately 11.816 N. I hope this answer doesn't weigh you down too much!
To find the acceleration of the box, we need to calculate the net force acting on it. The net force is the sum of the applied force and the force of friction.
Step 1: Calculate the force of friction (F_friction) between the box and the floor.
F_friction = coefficient of kinetic friction * normal force
The normal force (Fn) can be calculated as the weight of the box (mass * gravity):
Fn = mass * gravity
Fn = 17 kg * 9.8 m/s^2
Fn = 166.6 N
F_friction = 0.24 * 166.6 N
F_friction = 39.984 N
Step 2: Calculate the net force (F_net) acting on the box.
F_net = F_applied - F_friction
F_applied = 88.9 N (given)
F_net = 88.9 N - 39.984 N
F_net = 48.916 N
Step 3: Calculate the acceleration (a) of the box.
Using Newton's second law: F_net = mass * acceleration
48.916 N = 17 kg * acceleration
Acceleration (a) = 48.916 N / 17 kg
a = 2.875 m/s^2
Therefore, the acceleration of the box is 2.875 m/s^2.
To find the acceleration of the box being pulled, we can use Newton's second law of motion. This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Step 1: Find the net force acting on the box.
The net force can be calculated by subtracting the force of friction from the applied force.
Net force (F_net) = Applied force (F) - Force of friction (F_friction).
Step 2: Calculate the force of friction.
The force of friction can be found using the formula:
Force of friction (F_friction) = coefficient of friction (μ) × normal force (N),
where the normal force is equal to the weight of the box.
Normal force (N) = mass (m) × acceleration due to gravity (g).
Step 3: Calculate the acceleration.
Using Newton's second law, we can rewrite it as:
F_net = m × a,
where F_net is the net force calculated in step 1 and m is the mass of the box.
Solving for acceleration (a):
a = F_net / m.
Now let's plug in the given values to solve the problem:
Mass of the box (m) = 17 kg.
Applied force (F) = 88.9 N.
Angle (θ) = 56°.
Coefficient of kinetic friction (μ) = 0.24.
Acceleration due to gravity (g) = 9.8 m/s^2.
Step 1: Find the net force acting on the box.
Net force (F_net) = F - F_friction.
Step 2: Calculate the force of friction.
Normal force (N) = m × g.
Force of friction (F_friction) = μ × N.
Step 3: Calculate the acceleration.
a = F_net / m.
By following these steps and plugging in the given values, we can find the acceleration of the box.