The cart of mass 10 kg shown above moves without frictional loss on a level table. A 30 N force pulls on the cart horizontally to the right. At the same time, a 10 N force at an angle of 60° above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart?
Answer
0.5 m/s2
1.6 m/s2
2.0 m/s2
2.5 m/s2
2.6 m/s2
0.5 m/s^2
To find the magnitude of the horizontal acceleration of the cart, we need to determine the net horizontal force acting on the cart and then use Newton's second law of motion, which states that the net force is equal to the mass of an object multiplied by its acceleration.
First, let's find the horizontal components of the two forces acting on the cart:
- The 30 N force pulling to the right is already horizontal, so its horizontal component is simply 30 N.
- The 10 N force at an angle of 60° above the horizontal can be broken down into its horizontal and vertical components using trigonometry. The horizontal component can be found using the cosine function:
Horizontal component = 10 N * cos(60°)
Horizontal component = 10 N * 1/2
Horizontal component = 5 N
Now, let's determine the net horizontal force by adding the two horizontal components:
Net horizontal force = 30 N - 5 N
Net horizontal force = 25 N
Finally, we can calculate the horizontal acceleration using Newton's second law:
Net horizontal force = mass * acceleration
We have a mass of 10 kg, so:
25 N = 10 kg * acceleration
Simplifying the equation:
acceleration = 25 N / 10 kg
acceleration = 2.5 m/s^2
Therefore, the magnitude of the horizontal acceleration of the cart is 2.5 m/s^2.
To find the magnitude of the horizontal acceleration of the cart, we first need to determine the net force acting on the cart. The net force is the vector sum of all the forces acting on the cart.
Given:
Mass of the cart (m) = 10 kg
Horizontal force pulling to the right (F1) = 30 N
Force pulling to the left at an angle of 60° above the horizontal (F2) = 10 N
To find the horizontal acceleration of the cart, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
First, let's resolve the force F2 into its horizontal (Fx) and vertical (Fy) components. The horizontal component (Fx) will be F2 * cos(60°), and the vertical component (Fy) will be F2 * sin(60°).
Fx = F2 * cos(60°) = 10 N * cos(60°) = 10 N * 0.5 = 5 N
Fy = F2 * sin(60°) = 10 N * sin(60°) = 10 N * √(3/2) = 10 N * √3 / 2
Now, let's calculate the net force acting on the cart in the horizontal direction.
Net horizontal force (Fnet) = F1 - Fx
Fnet = 30 N - 5 N = 25 N
Next, we can calculate the horizontal acceleration (a) using Newton's second law.
Fnet = ma
25 N = 10 kg * a
a = 25 N / 10 kg
a = 2.5 m/s²
Therefore, the magnitude of the horizontal acceleration of the cart is 2.5 m/s².
So, the correct answer is 2.5 m/s².