The problem from the image involves a block of mass $m = 5 \, \text{kg}$ being pulled on a horizontal surface by a force $F = 25 \, \text{N}$, which is applied at an angle of $37^\circ$ to the horizontal. The coefficient of kinetic friction between the block and the surface is $\mu_k = 0.1$, and the gravitational acceleration is $g = 10 \, \text{m/s}^2$.

We are asked to find:

1. The normal force ($N$).
2. The frictional force ($f_k$).
3. The acceleration ($a$) of the block.

Step 1: Calculate the normal force ($N$)

The normal force is the force exerted by the surface to support the block’s weight, but here, the vertical component of the applied force $F$ reduces the normal force.

The vertical component of $F$ is: $F_y = F \sin(37^\circ) = 25 \times 0.6 = 15 \, \text{N}$

The gravitational force on the block is: $W = mg = 5 \times 10 = 50 \, \text{N}$

Thus, the normal force is: $N = W - F_y = 50 - 15 = 35 \, \text{N}$

Step 2: Calculate the kinetic friction force ($f_k$)

The kinetic friction force is given by: $f_k = \mu_k N = 0.1 \times 35 = 3.5 \, \text{N}$

Step 3: Calculate the acceleration ($a$)

First, we need the horizontal component of the applied force $F$: $F_x = F \cos(37^\circ) = 25 \times 0.8 = 20 \, \text{N}$

The net force acting on the block in the horizontal direction is: $F_{\text{net}} = F_x - f_k = 20 - 3.5 = 16.5 \, \text{N}$

Using Newton’s second law ($F = ma$), we can find the acceleration: $a = \frac{F_{\text{net}}}{m} = \frac{16.5}{5} = 3.3 \, \text{m/s}^2$

Summary of results:

• a) Normal force, $N = 35 \, \text{N}$
• b) Frictional force, $f_k = 3.5 \, \text{N}$
• c) Acceleration, $a = 3.3 \, \text{m/s}^2$

Would you like further details or have any questions?

Here are 5 related questions you might find helpful:

1. How does the angle of force application affect the normal force and friction?
2. What would happen to the acceleration if the friction coefficient were higher?
3. How does the weight of the object influence the frictional force?
4. What is the relationship between applied force and acceleration in the presence of friction?
5. How would the acceleration change if the force were applied horizontally instead of at an angle?

Tip: Always resolve forces into their components when dealing with forces applied at angles.