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Mechanics · Part 2 of 3
24 exam-style questions with model answers, plus 32 quick multi-choice questions — every question on this part of the standard, grouped by the 8 pages of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
A student has a mass of kg.
Calculate their weight on Earth, where m s−2.
A kg box is pushed along a horizontal bench with a force of N. Friction of N opposes the motion.
Calculate the net force on the box, and explain why the normal force from the bench is equal to the box's weight in this situation.
A skydiver jumps from a plane. She accelerates downward at first, but after some time she falls at a constant velocity known as terminal velocity.
Using free-body diagrams and Newton's laws, explain fully how the forces on her change from the moment she jumps until she reaches terminal velocity, and explain what happens to those forces immediately after she opens her parachute.
Two forces act on an object: N to the right and N to the left.
Calculate the net force.
A yacht is acted on by a N force from the wind pushing it east and a N force from the current pushing it south.
Calculate the size and direction of the resultant force, and explain why the resultant is not simply N.
Two tugboats tow a ship. Each pulls with a force of kN, and the two cables make an angle of with each other, symmetrically about the ship's forward direction.
Using a scale diagram or trigonometry, determine the resultant force on the ship. Then explain fully how the resultant would change if the angle between the cables were increased toward , and why tug crews try to keep the angle small.
A force of N acts at above the horizontal.
Calculate its horizontal component.
A kg crate rests on a ramp inclined at to the horizontal.
Calculate the component of the crate's weight acting down the slope and the normal force from the ramp. Explain why the normal force is less than the crate's weight.
A student must move a heavy suitcase across a floor. She can either push it with a force of N directed below the horizontal, or pull it with the same N force at above the horizontal. The suitcase has a mass of kg.
Analyse both options. Calculate the horizontal driving force and the normal force in each case, and explain fully which method makes the suitcase easier to move.
A net force of N acts on an object of mass kg.
Calculate the acceleration of the object.
A kg car experiences a driving force of N and resistive forces totalling N.
Calculate the car's acceleration. Then explain what happens to the acceleration as the car speeds up, if the driving force stays constant.
A student says: "Newton's third law says that when a horse pulls a cart, the cart pulls back on the horse with an equal force. The two forces are equal and opposite, so they must cancel out and the cart can never move."
Explain fully why the cart does in fact accelerate. Your answer should identify the third-law pairs involved and explain the difference between a third-law pair and balanced forces.
A kg ball on a string moves in a horizontal circle of radius m at m s−1.
Calculate the centripetal force acting on the ball.
A kg car rounds a bend of radius m at a constant m s−1.
Calculate the centripetal force required, name the force that provides it, and explain why the car is accelerating even though its speed is constant.
A driver takes a corner of radius m at km h−1 in the dry with no difficulty. The following week, in wet conditions on the same corner at the same speed, the car slides toward the outside of the bend and off the road.
The car has a mass of kg. Calculate the centripetal force required, then explain fully why the car left the road, referring to Newton's laws. Explain also why a passenger felt thrown toward the outside of the car.
A force of N is applied at right angles to a door handle m from the hinges.
Calculate the torque about the hinges.
A student cannot undo a tight bolt using a m spanner with a force of N. She fits a m pipe over the handle and applies the same force at the end of it.
Calculate the torque in each case, and explain why the longer lever succeeds.
A gate is m wide and hinged on its left edge. A child pushes with a force of N at the outer edge, but pushes at to the plane of the gate rather than perpendicular to it.
Calculate the torque produced. Explain fully why this is less than the torque from a perpendicular push of the same size, and explain why pushing a gate near its hinges is ineffective no matter how hard you push.
A seesaw is pivoted at its centre. A force of N acts downward m to the left of the pivot.
Calculate the torque this force produces about the pivot, and state its direction.
A uniform metre rule is pivoted at the cm mark. A N weight hangs at the cm mark.
Calculate where a N weight must hang to balance the rule, and explain why the weight of the rule itself can be ignored in this calculation.
A uniform diving board of mass kg and length m is bolted to the ground at its left end (support A) and rests on a roller support (support B) m from that end. The rest of the board projects over the water. A kg diver stands at the free right-hand end.
Calculate the forces at supports A and B. Explain fully what the sign of the force at A means physically, and why the bolt at A is necessary.
A spring is stretched by m when a force of N is applied.
Calculate the spring constant.
A spring has an unstretched length of cm. A kg mass hung from it stretches it to cm.
Calculate the spring constant and the elastic potential energy stored at that extension.
A student loads a spring with increasing masses and plots force against extension. The graph is a straight line through the origin up to a force of N and an extension of m, after which it curves upward less steeply. When the student removes all the loads after reaching N, the spring no longer returns to its original length.
Explain fully what the graph shows. Determine the spring constant, explain what has happened beyond N, and explain how the energy stored at m compares with the energy stored at m.