力及其效應：向量圖與自由體圖：練習題

A student uses a lever to lift a heavy load. The load has a weight of 600 N and is located 0.2 m from the pivot. The student applies a force at a distance of 1.5 m from the pivot on the opposite side. Calculate the minimum force the student must apply to just lift the load, assuming the lever is in rotational equilibrium.

A student uses a vector diagram to resolve a single force of 100 N into two perpendicular components. If one component is 60 N, calculate the magnitude of the other component using a scale drawing or calculation.

A uniform beam is balanced horizontally on a pivot. A 40 N weight is placed 0.60 m to the left of the pivot. A second weight, W, is placed 0.80 m to the right of the pivot to maintain equilibrium. Calculate the value of W and identify which principle is being applied.

A rectangular crate of mass 50 kg is being pushed across a floor. The pusher applies a horizontal force of 200 N. The friction between the crate and the floor is 150 N. Using a free body diagram approach, determine the acceleration of the crate.

A student uses a scale drawing to determine the resultant of two perpendicular forces. A force of 12.0 N acts due North and a force of 5.0 N acts due East. What is the magnitude of the resultant force, and what is the angle measured clockwise from North?

A uniform beam is balanced at its centre. A force of \(15\text{ N}\) is applied downwards at a distance of \(40\text{ cm}\) from the pivot. Calculate the magnitude of the force required to maintain rotational equilibrium if it is applied at a distance of \(1.2\text{ m}\) on the opposite side.