Numerade

Questions asked

INSTANT ANSWER

75 A ball of mass \( 250 \mathrm{~g} \) rolling on a horizontal floor with a speed \( 4.00 \mathrm{~ms}^{-1} \) hits a wall and bounces with the same speed, as shown in the diagram. a What is the magnitude and direction of the momentum change of the ball? b Is momentum conserved here? Why or why not?

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ANSWERED

Sai Sai

Numerade educator

15 A car of weight 1.4 × 10^4 N is moving up an incline at a constant speed of 6.2 m s^-1. The incline makes an angle of 5.0° to the horizontal. A frictional force of 600 N acts on the car in a direction opposite to the velocity. a i State the net force on the car. ii Calculate the force F pushing the car up the incline. b The power supplied by the car is 15 kW. Determine the efficiency of the car engine in pushing the car uphill. c The car is now allowed to roll down the incline from rest with the engine off. The only resistance force on the car is assumed to be proportional to speed. On a copy of the axes below, draw sketch graphs to show the variation with time of: i the speed of the car ii the acceleration of the car.

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INSTANT ANSWER

15 A car of weight \( 1.4 \times 10^{4} \mathrm{~N} \) is moving up an incline at a constant speed of \( 6.2 \mathrm{~ms}^{-1} \).The incline makes an angle of \( 5.0^{\circ} \) to the horizontal. A frictional force of \( 600 \mathrm{~N} \) acts on the car in a direction opposite to the velocity. a i State the net force on the car. [1] ii Calculate the force \( F \) pushing the car up the incline. b The power car uphill. [3]

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AWAITING AN EDUCATOR

14. It is proposed to launch projectiles of mass \( 8,0 \mathrm{~kg} \) from satellites in space in order to destroy incoming ballistic missiles. The launcher exerts a force on the projectile that varies with time according to the graph. The impulse delivered to the projectile is \( 2.0 \times 10^{3} \mathrm{~N} \). The projectile leaves the launcher in \( 0.20 \mathrm{~s} \). a Estimate: [1]

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INSTANT ANSWER

13 A toy helicopter has mass \( m=0.30 \mathrm{~kg} \) and blade rotors of radius \( R=0.25 \mathrm{~m} \). It may be assumed that as the blades turn, the air exactly under the blades is pushed downwards with speed \( v \). The density of air is \( \rho=1.2 \mathrm{~kg} \mathrm{~m}^{-3} \). a i Show that the force that the rotor blades exert on the air is \( \rho \pi R^{2} v^{2} \). [3] ii Hence estimate the speed \( v \) when the helicopter just hovers. [2] \( \mathbf{b} \) Determine the power generated by the helicopter's motor when it just hovers as in \( \mathbf{a} \). [2] c The rotor blades now move faster pushing air downwards at a speed double that found in a.The helicopter is raised vertically a distance of \( 12 \mathrm{~m} \). Estimate: [2] i the time needed to raise the helicopter. ii the speed of the helicopter after it is raised \( 12 \mathrm{~m} \). [2] iii the work done by the rotor in raising the helicopter. [1]

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ANSWERED

Rahul Kumar

Numerade educator

12 A stone of mass 0.20 kg is thrown with speed 22 m s-1 from the edge of a cliff that is 32 m above the sea. The initial velocity of the stone makes an angle of 35° with the horizontal. Air resistance is neglected. a i Determine the horizontal and vertical components of the initial velocity. [2] ii Sketch graphs showing the variation with time of the horizontal and vertical components of velocity. [2] b i Calculate the maximum height above the cliff reached by the stone. [3] ii State the net force on the stone at the highest point in its path. [1] c i Using conservation of energy, determine the speed of the stone as it hits the sea. [2] ii Hence or otherwise, determine the time it took the stone to reach the surface of the sea. [2] The graph shows the path followed by this stone, until just before hitting the sea, in the absence of air resistance. d i On a copy of the axes above, draw the path of the stone in the presence of an air resistance force opposite to the velocity and proportional to the speed. [3] ii State and explain one difference between your graph and the graph above. [2]

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INSTANT ANSWER

11 In a factory blocks of ice slide down a smooth curved path \( A B \) and then on to a rough horizontal path starting at \( B \). The length of the curved path AB is \( s \); the block of ice takes time \( t \) to move from A to B. a Explain why, for the motion of the block from A to B: i the formula \( s=\frac{1}{2} g t^{2} \) does not apply. [1] ii the formula \( v=\sqrt{2 g h} \) does apply. [1] b A block of ice of mass \( 25 \mathrm{~kg} \) slides from A to B. The speed of the block at B is \( v_{\mathrm{B}}=4.8 \mathrm{~ms}^{-1} \). Calculate the height \( h \). [3] c i The coefficient of dynamic friction between the block of ice and the rough surface BC is \( 0.45 \). [2] Show that the distance \( \mathrm{BC} \) at which the block of ice is brought to rest is \( 2.7 \mathrm{~m} \). ii Calculate the time it takes the block of ice to cover the distance BC. d The factory also produces blocks of ice of mass \( 50 \mathrm{~kg} \) that slide down the same path starting at \( A \). Predict, for this heavier block of ice, the speed at \( B \) and the stopping distance BC. (The coefficient of friction stays the same.) [3]

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ANSWERED

Pritesh Ranjan

Numerade educator

11 In a factory blocks of ice slide down a smooth curved path AB and then on to a rough horizontal path starting at B. The length of the curved path AB is s; the block of ice takes time t to move from A to B. a Explain why, for the motion of the block from A to B: i the formula s=½gt² does not apply. [1] ii the formula v= ?2gh does apply. [1]

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INSTANT ANSWER

83 A rocket in space where gravity is negligible has a mass (including fuel) of \( 5000 \mathrm{~kg} \). It is desired to give the rocket an average acceleration of \( 15.0 \mathrm{~ms}^{-2} \) during the first second of firing the engine.The gases leave the rocket at a speed of \( 1500 \mathrm{~ms}^{-1} \) (relative to the rocket). Estimate how much fuel must be burnt in that second.

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INSTANT ANSWER

81 The diagram shows the variation with time of the force exerted on a ball as the ball came into contact with a spring. a For how long was the spring in contact with the ball? b Estimate the magnitude of the change in momentum of the ball. c What was the average force that was exerted on the ball?

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melanie s.