A 40-kg cart on a horizontal floor is being pulled to the right by a 200 N force at 450 from the horizontal. The cart is rolling without friction. The normal force on the cart is closest to

To find the normal force on the cart, we need to consider the forces acting on it. The cart has a weight due to gravity and is subject to the vertical component of the applied force.

1. **Weight of the cart (W)**:
   \[
   W = m \cdot g = 40 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 392.4 \, \text{N}
   \]

2. **Vertical component of the applied force (F_v)**:
   The applied force is 200 N at an angle of 45° from the horizontal.
   \[
   F_v = F \cdot \sin(\theta) = 200 \, \text{N} \cdot \sin(45^\circ) = 200 \, \text{N} \cdot \frac{\sqrt{2}}{2} \approx 141.42 \, \text{N}
   \]

3. **Normal force (N)**:
   The normal force acts upward, balancing the weight of the cart and the vertical component of the applied force. Thus, the normal force is given by:
   \[
   N = W - F_v = 392.4 \, \text{N} - 141.42 \, \text{N} \approx 250.98 \, \text{N}
   \]

The normal force on the cart is closest to **251 N**.

### Do you want details or have any questions?

Here are some related questions you might consider:
1. How does the angle of the applied force affect the normal force?
2. What would happen to the normal force if the angle increased to 60°?
3. How would friction change the normal force calculation?
4. What are the implications of a heavier cart on the normal force?
5. How do you calculate the net force acting on the cart horizontally? 

**Tip:** Always resolve forces into their components when dealing with angled forces; it simplifies calculations significantly.

A 40-kg cart on a horizontal floor is being pulled to the right by a 200 N force at 45° from the horizontal. The cart is rolling without friction. The normal force on the cart is closest to?

Explore how to calculate the normal force acting on a 40-kg cart being pulled by a 200 N force at a 45° angle on a horizontal surface. This solution covers key physics concepts including force components and equilibrium, providing a clear calculation resulting in a normal force of approximately 251 N. Ideal for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation