Force, Work And Power Independent Study Questions

Force, Work and Power Independent Study Questions

Essential AS Physics for OCR

1) A child of weight 200N sits on a seesaw at a distance of 1.2m from the pivot at the centre. The seesaw is balanced by a second child sitting on it at a distance of 0.8m from the centre. Calculate the weight of the second child, 2) A meter rule pivoted at its centre of gravity supports a 3.0N weight at its 5.0cm mark, a 2.0N weight at its 25cm mark and a weight W at its 80cm mark a) Sketch a diagram to represent this situation b) Calculate the weight W. 3) In question 2, the 3.0N weight and the 2 N weights are swapped with each other. Sketch the new arrangement and work out the new distance of weight W from the pivot. 4) A uniform metre rule supports a 4.5N weight at its 100mm mark. This rule is balanced horizontally on a horizontal knife edge at its 340mm mark. Sketch the arrangement and calculate the weight of the rule.

1) A meter rule of weight 1.2N rests horizontally on two knife-edges at the 100 mm mark and the 800mm mark. Sketch the arrangement and calculate the support force on the rule due to each knife-edge. 2) A uniform beam of weight 230N and of length 10m rests horizontally on the tops of two brick walls 8.5m apart, such that a length of 1.0m projects beyond one wall and 0.5m beyond the other wall (Fig 2.14) 1.0m 8.5m 0.5m

Calculate a) The support force of each wall on the beam b) The force of the beam on each wall 3) A uniform bridge span of weight 1200kN and of length 17.0m rests on a support of width 1.0m at ether end. A stationary lorry of weight 60kN is the only object on the bridge. Its centre of gravity is 3.0m from he centre of the bridge (Fig 2.15). Calculate the supportive force on the bridge at each end.

4) A uniform plank of weight 150N and of length 4.0m rests horizontally on two bricks. One of the bricks is at the end of the beam. The other brick is 1.0m from the other end of the plank. a) Sketch the arrangement and calculate the support force on the plank from each brick b) A child stands on the free end of the beam and just causes the other end to lift off its support. Sketch this arrangement and calculate the weight of the child.

1) A ball of mass 0.50kg was thrown directly up at a speed of 6.0 ms-1. Calculate : a)fIts kinetic energy at 6ms-1 b) Its maximum gain of potential energy c) Its maximum height gain 2) A ball of mass 0.20kg, at a height of 1.5m above a table, is released from rest and it rebounds to a height of 1.2m above the table. Calculate: ai) The loss of potential energy on descent aii) The gain of [potential energy at maximum rebound height 3) A cyclist of mass 80kg (including bicycle) freewheels from rest 500m down a hill. The foot of the hill is 20 m lower than the cyclists starting point, and the cyclist reaches a speed of 12ms-1 at the foot of the hill. Calculate: ai) The loss of potential energy aii)The gain of kinetic energy of the cyclist and the cycle bi) The work done against friction and air resistance during the descent bii)The average resistive force during the descent 4) A fairground vehicle of total mass 1200kg, moving at a speed of 2ms-1, descends through a height of 50m to reach a speed 0f 28ms-1, after travelling a distance of 75m along the track. Calculate: a) Its loss of potential energy b) Its initial kinetic energy c) Its kinetic energy after the descent d) The work done against friction e) The average frictional force on it during the descent Page 63 g = 9.8 ms-2

1) A student of weight 450N climbed 2.5m up a rope in 18s. Calculate: a) The gain of potential energy of the student b) The energy transferred per second 2) Calculate the power of the engines of an aircraft at a speed of 250 ms-1, if the total engine thrust to maintain this speed is 2.0MN. 3) A rocket of mass 5800kg accelerates vertically from rest to a speed of 220 ms-1, in 25s. Calculate: a) Its gain in potential energy b) Its gain of kinetic energy c) The power output of the engine, assuming no energy is wasted due to air resistance. 4) Calculate the height through which a 5kg mass would need to be dropped to loose the same energy as a 100W light bulb would use in 1 min.

1) Calculate the pressure exerted by a paving stone of density 2500kgm-3 and of dimensions 0.8mx0.8mx0.05m when the stone rests flat on a smooth horizontal surface. 2) Calculate the force due to the atmosphere on the panes of a sealed double glazed window of dimensions 1.5mx0.8m which has a vacuum between the two panes. The mean value of atmospheric pressure = 101kPa. 3) The pressure in the tyres of a vehicle is 280kPa. The contact area of each of the four tyres on the ground is 0.012m2. Calculate the weight of the vehicle. 4) A hydraulic brake system has a master cylinder of area of cross section 5.0x10-4m2 and four slave cylinders, each of cross-sectional area 1.5x10-2m2. When a force of 120N is applied to the master cylinder, calculate: ai) The pressure in the system aii)The force on each slave cylinder b) The maximum distance moved by the slave piston, if the master piston moved a distance of 60mm.

Q2) A hydraulic lift is used in a garage to raise a vehicle to enable its underside to be repaired. The figure below shows how such a lift works. The maximum pressure of the fluid in the lift is 1.2 MPa.

a) The area of cross-section of each of the four “legs” of the lift is 9.0x10-3 m2. Calculate the maximum safe load the lift can raise if the lift platform has a weight of 1.5x104N. b) The lift is used to raise a vehicle of mass 2200kg through a height of 2.4m i) Calculate the gain of potential energy of the vehicle. ii) Calculate the work done by the hydraulic system to lift the wehicle by 2.4m iii) Account for the difference between your answer to (i) and (ii)

Physics 1 SAQ 5.4 A wheel barrow is loaded as shown in figure 5.9 A) Calculate the force that the gardener needs to exert to hold the legs off the ground B) What force is exerted by the ground on the legs of the wheelbarrow (taken both together) when the gardener is not holding the handles 0.20m

SAQ 5.7 The driving wheel of a car travelling at a constant velocity has a torque of 137Nm applied to its by the axle that drives the car (fig 5.14). The radius of the tyre is 0.18m. What is the driving force provided by this wheel.

SAQ 5.8 A chair stands on four feet, each of area 10cm2. The chair weighs 80N. Calculate the pressure it exerts on the floor. SAQ 5.9 Estimate the pressure you exert on the floor when you stand on both feet.

SAQ 6.1 In each of the following examples, explain whether or not any work is done by the force mentioned. A) You pull a heavy sack along rough ground B) Gravity pulls you downwards when you fall off a wall. C) The tension in a string pulls a conker when you whirl it around in a circle at a steady speed. D) The contact force of the bedroom floor stops you from falling into the room below.

SAQ 6.2 A man of mass 70kg climbs stairs of height 2.5m. How much work does he do against the force of gravity (g=9.8ms-2)

SAQ 6.3

A stone of weight 10N falls from the top of a 250m high cliff. A) How much work is done by the force of gravity in pulling the stone to the cliff foot. B) How much energy is transferred to the stone

SAQ 6.4

The crane shown in figure 6.4 lifts its 500N load to the top of the building. Distances are shown on the diagram. How much work is done by the crane.

50m 40m

SAQ 6.7

Which has more KE, a car of mass 500kg moving at 15ms-1, or a motorcycle of mass 250 kg moving at 30ms-1. SAQ 6.8

Calculate the change in kinetic energy of a ball of mass 200g when it bounces. Assume that it hits the ground with a speed of 15.8ms-1, and it leaves it at 12.2ms-1.

SAQ 6.9

Worked Example

A pendulum consists of a brass sphere of mass 5kg hanging from a long string (see figure 6.6). The sphere is pulled to the side so that it is 0.15m above its lowest position. It is then released. How fast will it be moving when it passes through the lowest point along its path?

Step 1: Calculate the loss in GPE as the sphere falls from its highest position.

∆Ep=mg∆h

∆Ep=5 x 9.8 x 0.15 ∆Ep=7.35J

Step 2: This tells us that the gain in the sphere’s energy is 7.35J. We can use this to calculate the sphere’s velocity. First calculate v2, then v:

½ mv2 = 7.35J v2=2x7.35J = 2.94m2s-2 5kg -2 -1 v = √2.94m2s = 1.71ms

SAQ 6.10 How much gravitational potential; energy is lost by an aircraft of mass 80000kg if it descends from an altitude of 10000m to an altitude of 1000m? What happens to this energy if the pilot keeps the speed the same.

SAQ 6.11 A high diver reaches a highest point in her where her centre of gravity is 10m above the water. Assuming that all her gravitational potential energy becomes kinetic energy during the dive. Calculate her velocity as she enters the water. SAQ 6.12 How much work is done by a 50kW car engine in 1 minute.

1) How much work do you do when you lift a heavy book of mass 2 kg from the floor to a shelf 1.8m above the floor? (take g to be 9.8ms-2).

2) The car shown in figure 6.10 weighs 5000N. It travels 1km along a sloping road, ending up 100m higher than its starting position. Its engine provides a forward motive force of 2kN a) How much work is done by the force of the engine b) How much work is done against the force of gravity c) What other force is the engine working against?

Normal reaction

Force of enginefriction 100m2kN 1km

Weight 5kN

3) A car engine does 4200kJ of work in one minute. What is its power output, in kilowatts?

4) A cars engine provides a motive force of 700N when the car is moving at its top speed of 40ms-1. a) How much work does the cars engine do in each second. b) What is the engines power output?

5) In an experiment to measure a students power, she times herself running up a flight of stairs. Use the data below to work out her useful power. ●number of steps = 28 ●height of each step = 20cm ●time taken = 5.4s ●mass of student = 55kg ●acceleration due to gravity = 9.8ms-2

1) Figure 5.15 shows a beam with four forces acting on it. a) For each force, calculate the moment of the force about point P. b) Say whether each moment is clockwise or anticlockwise. c) Are the moments of the forces balanced? F4 = 20N

F1= 10N

25cm 25cm 25cm

2) Force F shown in F3 = 10N figure 5.16 has a moment of 40Nm about the pivot. What is the F2 = 10N magnitude of F?

3) A force of 20N acts as shown to balance the beam in figure 5.17. At what distance x from the pivot point must it act?

4N 0.5m 0.5m X

10N 20N 4) A cantilever balcony is shown in figure 5.18. Using the data given on the diagram, calculate the value of the support force S. S

1m 3m 800N 1800N