A man drags a 68.0-kg crate across the floor at a constant velocity by pulling on a strap attached to the bottom of the crate. The crate is tilted 23.5° above the horizontal, and the strap is inclined 55.0° above the horizontal. The center of gravity of the crate coincides with its geometrical center, as indicated in the drawing. Find the magnitude of the tension in the strap.
I got the answers 221.85, 361.96. 941.56. but they are all incorrect. Not sure what I am doing wrong in my arithmetic.
Not sure either. Are we on a ramp?
To find the magnitude of the tension in the strap, we can break the force into horizontal and vertical components.
1. Find the weight of the crate: The weight (force due to gravity) can be calculated using the formula:
weight = mass * gravity
Given that the mass of the crate is 68.0 kg and the acceleration due to gravity is 9.8 m/s^2, we can calculate the weight of the crate.
2. Break the weight force into components: Since the crate is tilted at an angle of 23.5° from the horizontal, we can break down the weight force into two components: one parallel to the incline (F_parallel) and one perpendicular to the incline (F_perpendicular). The angle between the incline and the vertical is the complement of 23.5°.
3. Calculate the normal force: The normal force is the perpendicular force exerted by a surface to support the weight of the object. It acts perpendicular to the incline and balances the component of the weight force perpendicular to the incline.
4. Calculate the tension force in the strap: The tension in the strap acts parallel to the incline and balances the component of the weight force parallel to the incline.
5. Calculate the tension force magnitude: To find the magnitude of the tension, we need to consider the equilibrium condition. Since the crate is being dragged at a constant velocity, the net force in the horizontal direction (along the incline) must be zero. Using this information, we can write an equation that relates the tension force to the weight force component parallel to the incline.
By following these steps, you can correctly calculate the magnitude of the tension in the strap.