A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20.0°, and the man pulls upward with a force F→ whose direction makes an angle of 30.0° with the ramp (Fig. E4.4). (b) How large will the component Fy perpendicular to the ramp be then?

Verified step by step guidance

1. Identify the angle between the force F and the ramp, which is given as 28.0°.
2. Determine the angle of the ramp with the horizontal, which is given as 15.0°.
3. Calculate the angle between the force F and the horizontal by adding the ramp angle and the angle between the force and the ramp: 28.0° + 15.0°.
4. Use trigonometry to find the component of the force F perpendicular to the ramp. This component is given by Fy = F * sin(θ), where θ is the angle between the force and the horizontal.
5. Substitute the values into the equation to find Fy: Fy = F * sin(43.0°).

Key Concepts

Components of Force

Forces can be broken down into components that act along specific directions. In this scenario, the pulling force F can be resolved into two components: one parallel to the ramp and one perpendicular to it. Understanding how to decompose forces into their components is essential for analyzing the effects of the applied force on the trunk's motion.

Trigonometric Functions

Trigonometric functions, such as sine and cosine, are used to relate the angles and sides of right triangles. In this problem, the angles of the ramp and the pulling force allow us to calculate the perpendicular component of the force using the sine function. This mathematical relationship is crucial for determining how much of the force acts in the direction perpendicular to the ramp.

Newton's Laws of Motion

Newton's Laws of Motion describe the relationship between the motion of an object and the forces acting on it. The first law states that an object at rest will remain at rest unless acted upon by a net force. In this context, understanding how the applied force affects the trunk's movement up the ramp is key to solving the problem, as it involves analyzing the net forces acting on the trunk.