A crate with a weight of 300 N accelerates along a frictionless surface as the it is pulled with a force of F = 15.0 N as shown in the figure. What is the horizontal acceleration of the crate?

To determine the horizontal acceleration of the crate, we can apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). In this case, we need to find the acceleration of the crate when a force of 15.0 N is applied to it.

Step-by-Step Calculation

First, we need to find the mass of the crate. We know that weight (W) is related to mass (m) and gravitational acceleration (g) by the formula:

W = m × g

In this scenario, the weight of the crate is given as 300 N. The standard acceleration due to gravity (g) is approximately 9.81 m/s². We can rearrange the formula to solve for mass:

m = W / g

Substituting the known values:

m = 300 N / 9.81 m/s² ≈ 30.58 kg

Calculating Acceleration

Now that we have the mass of the crate, we can use Newton's second law to find the acceleration (a). The net force (F_net) acting on the crate is the applied force minus any opposing forces. Since the surface is frictionless, the only force we consider is the applied force of 15.0 N:

F_net = F

Now we can apply Newton's second law:

F_net = m × a

Substituting the values we have:

15.0 N = 30.58 kg × a

To find the acceleration, we rearrange the equation:

a = F_net / m

Plugging in the numbers:

a = 15.0 N / 30.58 kg ≈ 0.49 m/s²

Final Result

The horizontal acceleration of the crate is approximately 0.49 m/s². This means that for every second that the force is applied, the crate's speed will increase by about 0.49 meters per second.

Real-World Application

This principle is not just theoretical; it applies to many real-world situations. For example, when you push a shopping cart, the acceleration you feel depends on how hard you push (the force) and how heavy the cart is (the mass). If the cart is empty, it accelerates faster than when it's full, just like our crate on a frictionless surface.