Forces — Numerical Practice
Covers: resultant force and F = ma, the spring constant k = F/x, and moments (including the principle of moments). 20 questions.
A. Resultant Force and F = ma
A resultant force of 20 N acts on a 4 kg object. Calculate its acceleration.
A 3 kg object accelerates at 6 m/s². Calculate the resultant force acting on it.
A box has a driving force of 50 N forward and a friction force of 20 N backward acting on it. Calculate the resultant force.
A 1000 kg car experiences a resultant force of 2500 N. Calculate its acceleration.
An 8 kg object needs an acceleration of 3 m/s². The driving force is 40 N. Calculate the size of the resistive force also acting on it.
Two forces of 15 N and 9 N act in opposite directions on an object. Calculate the resultant force, stating its direction.
A 2000 kg car accelerates from rest to 15 m/s in 5 s. Calculate the resultant force needed to produce this acceleration.
B. Spring Constant
A spring extends by 4 cm under an 8 N load (within the limit of proportionality). Calculate its spring constant.
A spring has a spring constant of 3 N/cm. Calculate its extension under a 15 N load.
Calculate the force needed to extend a spring of spring constant 4 N/cm by 7 cm.
Two identical springs each have a spring constant of 2.5 N/cm. Calculate the force needed to extend one of them by 6 cm.
A spring’s load-extension graph is a straight line through the origin up to a load of 10 N, where the extension is 5 cm; beyond this point the graph curves. Calculate the spring constant in the straight-line region, and explain what the curve beyond 10 N represents.
C. Moments
A force of 20 N acts at a perpendicular distance of 0.5 m from a pivot. Calculate the moment.
A moment of 15 N m is produced by a force acting at a perpendicular distance of 0.3 m from a pivot. Calculate the size of the force.
A see-saw balances with a 300 N person sitting 2 m from the pivot. Calculate the weight of a second person sitting 3 m from the pivot on the other side, for the see-saw to balance.
A beam pivots at its centre. A 20 N force acts 0.4 m from the pivot on the left. Calculate the force needed 0.8 m from the pivot on the right for the beam to balance.
A beam pivots at its centre. On the left: a 10 N force at 0.5 m and a 5 N force at 1 m from the pivot. Calculate the single force needed at 0.6 m from the pivot on the right for the beam to balance.
State the two conditions required for an object to be in equilibrium.
A door is opened by pushing with a force of 15 N at a perpendicular distance of 0.8 m from the hinge. Calculate the moment produced. If the same moment is instead produced by pushing at 0.4 m from the hinge, calculate the force needed.
A spanner is used to turn a nut, with a force of 40 N applied perpendicular to the spanner at a distance of 0.15 m from the nut. Calculate the moment applied.
Mastery Test
A resultant force of 30 N acts on a 5 kg object. Calculate its acceleration.
A 6 kg object accelerates at 2.5 m/s². Calculate the resultant force.
Two forces of 45 N and 15 N act in opposite directions on an object. Calculate the resultant force.
A spring has a spring constant of 5 N/cm. Calculate its extension under a 20 N load.
A spring extends 6 cm under an 18 N load. Calculate its spring constant.
A force of 25 N acts at a perpendicular distance of 0.4 m from a pivot. Calculate the moment.
A see-saw balances with a 250 N person sitting 1.5 m from the pivot. Calculate the weight of a second person sitting 2.5 m from the pivot on the other side.
A beam pivots at its centre. A 12 N force acts 0.5 m from the pivot on the left. Calculate the force needed 0.3 m from the pivot on the right to balance the beam.
State the two conditions required for an object to be in equilibrium.
A door is pushed with a force of 20 N at a perpendicular distance of 0.6 m from the hinge. Calculate the moment produced.
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