Final answer:
The acceleration of a 40 kg box dragged across a frictionless horizontal surface by a rope at a 42° angle with a tension of 65 N can be found by resolving the tension into components and applying Newton's second law.
Step-by-step explanation:
The question involves determining the acceleration of a box being pulled on a frictionless surface, which is a classic physics problem involving Newton's second law of motion.
Step-by-step solution:
- First, resolve the tension into horizontal and vertical components since the force is at an angle to the horizontal. The horizontal component (Tx) is T*cos(42°), and the vertical component (Ty) will be T*sin(42°), where T is the tension in the rope.
- Since the surface is frictionless, only the horizontal component will affect the horizontal motion of the box. Therefore, we use Tx = T*cos(42°) to calculate the force in the horizontal direction.
- Apply Newton's second law, F = m*a, to find the acceleration (a). Rearrange to a = F/m and substitute in the horizontal component of the force for F.
- Calculate the numerical value of acceleration using the given values: a = (65 N * cos(42°)) / 40 kg.
By following these steps, you can find the box's acceleration on the frictionless surface.