The ENGAA 2020 paper in full: all 20 questions, each with its answer. ENGAA is the Engineering Admissions Assessment. Sit it cold under exam timing, mark it, then work back through anything you missed using the solutions below.
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Question 1
1 mark
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
Spring P has spring constant 1.0Ncm−1 and spring Q has spring constant 3.0Ncm−1. The two springs are connected in series. The springs are stretched by 6.0cm in total. What is the extension of spring P? (The springs have negligible mass and obey Hooke's law.)
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A single strand of wire has a radius of 2.0×10−4m and length 15m. The resistivity of the material from which the wire is made is 4.8×10−7Ωm. Twelve strands of this wire are connected in parallel to make a cable. What is the resistance of the cable?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A ray of light is directed into a semicircular transparent block, entering at P. The direction of the ray is adjusted until it strikes the centre of the flat face XY of the block at the critical angle and reflects to Q as shown.
The length of XY is L. The speed of light in air is c. What is the time taken by the light to travel from P to Q in the block?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A solid cube with sides of length 20 cm is made from material with density 2000kgm−3. The cube is suspended, in equilibrium, from an initially unstretched spring, and this results in the spring gaining strain energy of 3.2J. What is the spring constant of the spring? (gravitational field strength = 10Nkg−1; the spring obeys Hooke's law)
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A projectile is fired upwards from the ground at an angle of 60∘ to the vertical at a speed of 20ms−1. It travels a horizontal distance d and lands with a downwards vertical component of velocity of 4.0ms−1 on ground that is height h above the starting point of the projectile. What are d and h? (gravitational field strength = 10Nkg−1; assume that air resistance is negligible)
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A spaceship with mass 8.0×104kg travels at constant velocity and has 1.0×1012J of kinetic energy. An external impulse of 8.0×107kgms−1, lasting for 2.0s, is applied to the spaceship acting in the opposite direction to the motion of the spaceship. What is the average rate of loss of kinetic energy of the spaceship during the application of the impulse?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
The diagram shows a solid triangular prism.
The sides of the triangular cross section of the prism are of length x. The height of the prism is 3x. The uniform density of the prism is ρ. The gravitational field strength is g. What is the minimum pressure the prism can exert when it rests on level ground?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
An apple of mass ma is placed on a uniform metre rule with the centre of gravity of the apple at the 10cm mark. The rule is balanced on a pivot placed at the 35cm mark. The apple is replaced with an orange of mass mo. The rule now balances with the pivot at the 40cm mark. What is the ratio moma?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A cyclist travels at a constant speed of 12ms−1 on level ground. During this time the power needed to maintain a constant speed is 900W. The total weight of the cyclist and bicycle is 850N. The cyclist now cycles up a slope at the same constant speed. The slope is at an angle of 30∘ to the horizontal. What is the driving force on the bicycle as it travels up the slope? (Assume that the magnitude of the resistive forces is constant.)
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
Three identical resistors can be combined in four different arrangements. One of the arrangements has a resistance of 18Ω. A different arrangement has a resistance of 8.0Ω. What are the resistances of the other two arrangements? (All three resistors contribute to the total resistance in all arrangements.)
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A 4.0kΩ fixed resistor is connected in series with a light dependent resistor (LDR) across a 100V dc power supply. The current in the LDR is 5.0mA. The intensity of light falling on the LDR now decreases and the voltage across the fixed resistor changes by 50%. What is the change in the resistance of the LDR as a result of the change in intensity?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
An elastic cord with spring constant k is fixed to two points P and Q on the diameter of a ring so that the cord is taut but unstretched. The radius of the ring is r.
The midpoint of the cord is then pulled and fixed to a point on the ring halfway between P and Q. What is the energy stored in the elastic cord?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
An object of mass M experiences a resultant force of magnitude F. The force acts in a single horizontal direction with a magnitude that varies with time t according to F=X+Yt where X and Y are constants. The object is at rest at t=0. What is the magnitude of the momentum of the object at time t=T?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A trolley of mass 3.0kg is moving horizontally along a smooth track. Its displacement x from a point at time t is given by the equation: x=8+4t+2t2 where x is in metres and t is in seconds. How much work is done on the trolley between times t=0 and t=5.0s?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
The diagram shows a ray of light passing through three mediums, P, Q and R. The boundaries between the three mediums are parallel.
[diagram not to scale] The ratio of the speed of light in medium P to the speed of light in medium Q is 2:5 The ratio of the speed of light in medium Q to the speed of light in medium R is 3:6 What is the value of sinθ?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
Water in a wide river flows at a constant speed of 0.50ms−1. A swimmer swims around a square path of side 30m marked out by 4 posts R, S, T and U which are fixed to the river bed, as shown. The swimmer has a constant speed of 1.0ms−1 relative to the water.
How long does it take for the swimmer to swim around the square path once?
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
The stress in a steel cable increases with time and is then maintained at a constant value, as shown. The wire does not reach its limit of proportionality.
The table shows properties of the steel used in the cable and the dimensions of the cable.
Not in the current ESAT specification — included for completeness, but you won't be tested on it.
A cell has emf E and internal resistance r that varies with current I according to: r=kI2 where k is a constant. A variable resistor is connected to the terminals of the cell. The resistance of the variable resistor is adjusted. Which expression gives the resistance of the variable resistor, in terms of k and E, that causes maximum power dissipation in it?
