Question

What is the magnitude of the force, F, required to push the 10

kg block up the 15-degree inclined plane at a constant speed? Take
the coefficient of kinetic friction to be 0.25.

Answer 1

The magnitude of the force required to push the 10kg block up the 15-degree inclined plane at a constant speed is 121.66N. This force is calculated by taking into account the force of gravity pulling the block down the plane and the force of friction acting against the block. Step-by-step calculations are provided to find the normal force, force of friction, and the final magnitude of the required force.

Step-by-step explanation:

To find the magnitude of the force required to push the 10kg block up the 15-degree inclined plane at a constant speed, we need to consider the forces acting on the block. The force required will be equal to the force of gravity pulling the block down the plane plus the force of friction pushing against the block. The force of gravity can be calculated using the formula F = m * g, where m is the mass of the block (10kg) and g is the acceleration due to gravity (9.8m/s²).

The force of friction can be calculated using the formula F_f = μ_k * F_n, where μ_k is the coefficient of kinetic friction (0.25) and F_n is the normal force acting on the block. The normal force can be calculated as F_n = m * g * cos(theta), where theta is the angle of inclination (15 degrees in this case).

Next, we can calculate the normal force and the force of friction. Finally, we can add the force of gravity and the force of friction to find the magnitude of the force required.

Let's calculate step-by-step:

1. Calculate the force of gravity: F_g = m * g = 10kg * 9.8m/s² = 98N
2. Calculate the normal force: F_n = m * g * cos(theta) = 10kg * 9.8m/s² * cos(15°)
3. Calculate the force of friction: F_f = μ_k * F_n = 0.25 * F_n
4. Calculate the magnitude of the force required: F = F_g + F_f

Now, plug in the values and calculate:

1. Calculate the normal force: F_n = 10kg * 9.8m/s² * cos(15°) = 94.64N
2. Calculate the force of friction: F_f = 0.25 * 94.64N = 23.66N
3. Calculate the magnitude of the force required: F = 98N + 23.66N = 121.66N

Therefore, the magnitude of the force required to push the 10kg block up the 15-degree inclined plane at a constant speed is 121.66N.