State Newton’s Second Law.
At its launch, a rocket and its contents have a total mass of 151 000 kg. The engine produces an upward thrust of 3 550 000 N. Figure 1 below shows the rocket just after its launch.
Figure 1
Calculate the weight of the rocket at the launch.
Calculate the resultant force acting on the rocket during the launch.
Calculate the acceleration of the rocket at launch.
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Figure 1 shows a skier being pulled forward by rope at a constant velocity along a horizontal section between two ski runs. The tension in the rope is 50 N and the total mass of the skier is 85 kg.
Figure 1
State the name of each of the forces A – D acting on the skier in Figure 1.
Determine the magnitude of Force A and explain your answer.
The rope towing the skier suddenly brakes, so Force B no longer acts on the skier, however the skier continues to move forwards.
Force A remains constant.
By considering the horizontal forces now acting on the skier, explain whether the skier accelerates or decelerates after the tow rope breaks.
Assuming the magnitude of Force A remains constant, as determined in part (b), calculate the deceleration of the skier.
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A remote-controlled racing car has a mass of 0.60 kg. It can accelerate uniformly from rest to 5.2 m s–1 in 1.6 s.
Calculate the acceleration of the car.
Calculate the resultant force acting on the car when it is accelerating.
After 1.8 s the motor is switched off and the car decelerates uniformly until it stops. The deceleration of the racing car is 0.80 m s–2.
Given that the resistive force is the only force acting on the car once the motor is switched off, calculate the magnitude of this force.
Assuming that the resistive force was constant throughout the motion of the racing car, use your answer from part (b) to calculate the thrust from the motor when the racing car was accelerating.
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A brick of mass 1.5 kg is resting on the floor as shown in Figure 1.
Figure 1
Name the forces A and B acting on the block.
Explain how Newton’s first law can be applied to the forces acting on the brick.
A horizontal force is applied to the brick which causes it to accelerate at 0.2 m s−2.
Use Newton’s Second Law to calculate the size of the horizontal force which is applied to the brick.
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A block of wood of mass 5.2 kg, sitting on a smooth table, is acted upon by a force of 5.8 N as shown in Figure 1.
Figure 1
Calculate the expected acceleration of the wooden block, assuming there are no frictional forces acting between the block and the table.
The movement of the wooden block is investigated using a data logger.
The velocity-time graph obtained by the data-logger is shown in Figure 2 below.
Figure 2
Use the data in Figure 2 to calculate the actual acceleration of the wooden block.
Use the actual acceleration of the block, calculated in part (b), to calculate the resultant force acting on the block.
As the acceleration of the block in parts a) and b) are different, this shows that there is a resistive force acting between the block and the table.
Use your answer to part (c) to calculate the resistive force acting on the block
Remember that the block is being pulled with a force of 5.8 N.
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A 9.0 N force and a 5.0 N force act on a body of mass 3.0 kg at the same time.
Calculate the maximum and minimum accelerations that can be experienced by the body.
A fairground ride ends with the car moving up a ramp at a slope of 25° to the horizontal as shown in Figure 1.
Figure 1
The car carrying its maximum load of passengers has a total weight of 9.7 kN.
Show that the component of the weight acting parallel to the ramp is about 4.1 kN.
The mass of the fully loaded car is 950 kg.
Show that the force in part (b) will decelerate the car at about 4.3 m s–2.
The ride owner decides to use a shorter ramp and to install brakes on the car. The additional decelerating force provided by these brakes is 3400 N. The car enters the ramp at 33 m s–1.
Calculate the new stopping time.
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The Soyuz Spacecraft is used to transport astronauts to and from an orbiting space station. The spacecraft is made up of three sections as shown in Figure 1.
Figure 1
On leaving the space station the spacecraft is given an initial horizontal thrust of 2400 N.
Calculate the initial acceleration of the spacecraft during the firing of the thruster engines.
Newton’s Third Law refers to pairs of forces.
State one way in which a pair of forces referred to in Newton’s Third Law are the same and one way in which a pair of forces are different.
When the spacecraft returns to the Earth’s atmosphere the orbital module and the service module are separated from the descent module. This descent module has its speed greatly reduced by drag from the atmosphere.
Figure 2 shows two of the forces acting on the descent module as it travels down through the atmosphere.
Figure 2
State one reason why the two forces shown in Figure 2 are not a pair of forces as referred to in Newton’s Third Law.
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A boy throws a ball vertically upwards with a velocity of 13 m s–1 and lets it fall to the ground. Figure 1 shows a graph of velocity against time for the first few seconds of the ball’s motion.
Figure 1
Sketch on Figure 1 the variation of the ball’s velocity relative to the ground.
Figure 2 shows the ball deforming as it makes contact with the ground, just at the point where it is stationary for an instant and has reached maximum deformation.
Figure 2
Explain how Newton’s third law of motion applies to Figure 2.
A moment later the ball begins to move upwards.
Explain why there is a resultant upward force on the ball in Figure 2.
The ball has a mass of 65 g.
Calculate the maximum force exerted by the ground the moment the ball comes into contact with it.
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A van of mass 2200 kg pulls a trailer of mass 410 kg with a driving force of 3550 N. The van and trailer accelerate at 1.1 m s–2.
Calculate the resultant force on the van and trailer.
Calculate the resistive force on the van and trailer.
The resistive force acting on the trailer is equal to the resistive force acting on the van.
Use this information to calculate the force with which the van pulls the trailer.
When the van reaches its destination, a crate is lifted vertically from the trailer at a constant speed by a cable attached to a crane.
With reference to one of Newton’s laws of motion, explain why the tension, T, in the cable must be equal to the weight of the crate.
You may be awarded marks for the quality of written communication in your answer.
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Figure 1 shows the motion of a truck as it moves on a curved track.
Figure 1
The slope beyond position B is horizontal.
On the axes below, sketch a speed – time graph for the truck from its release at position A until it reaches position X, as shown in Figure 1.
Indicate on your graph the time when the truck is at position B.
You can assume that frictional forces are negligible.
Explain how Newton’s first law of motion is illustrated by the motion of the truck between B and X.
Figure 2 shows another truck moving freely down a ramp inclined at an angle to the horizontal.
Figure 2
The truck starts from rest at the top of the ramp and reaches point C. Friction and air resistance are negligible.
Discuss how the acceleration of the truck in Figure 2 differs from the acceleration of the truck in Figure 1.
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Two skateboarders X and Y are standing stationary on their skateboards as shown in Figure 1.
Figure 1
When X holds the ball, X remains still. When X throws a ball to Y, X moves to the left. When Y catches the ball, Y moves to the right and then eventually comes to rest.
Explain, using Newton’s three laws of motion, the motion of skateboarder X and the motion of the ball.
Ignore all effects of friction and air resistance.
Two people of the same mass are having a tug-of-war match. Each person tries to pull the other by leaning backwards, as shown in Figure 2.
Figure 2
Describe, using Newton’s laws, the resultant motion of the people pulling on the rope.
You may assume there is no friction.
In a different game of tug-of-war, the two players are on skateboards. Both skateboarders X and Y have a mass of 65 kg and and are 17 m apart, as shown in Figure 3.
Figure 3
X pulls on the rope and exerts a force of 40 N, whilst Y just holds the rope. Friction is ignored.
Show that it takes 7.4 seconds for both X and Y to meet.
Figure 4 shows two other people playing another game of tug-of-war. Person A has a mass of 60 kg and Person B has a mass 75 kg.
Figure 4
Both people have slightly different materials for the soles of their shoes. This means the overall friction force on Person A is 420 N and 21 N on Person B. Person A pulls on the rope with a force of 240 N, and Person B pulls on the rope with a force of 246 N. The rope has a mass of 2 kg.
Show that the resultant acceleration of both Person A, Person B and the rope is 3 m s–2 to the left.
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The set-up below shows three objects 
, 
and 
accelerating to the left at an acceleration a due to an applied force F such that the masses and do not move relative to mass .
The objects and are connected by an inextensible string that passes through a light, inextensible pulley as shown in Figure 1.
Figure 1
Derive an expression for F in terms of , , and g.
You may assume all surfaces to be smooth and the effects of friction neglected in the question.
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Videos of astronauts on the International Space Station are shared all over the world. Many science students excitedly watch as the astronauts float around their cabins, perform space walks and other duties.
Weightlessness is a term used to describe the experience of astronauts in orbit. Many early students of science have misconceptions about this term, particularly, that it means an absence of gravity. In fact, weightlessness is an effect of the astronauts being in a state of constant free fall.
By referring to Newton’s laws of motion, discuss the term ‘weightlessness’ as applied to astronauts in orbit.
In your answer, you may want to include:
Einstein considered the theoretical perspective of an astronaut in deep space and was able to come up with fundamental revisions to Newton’s ideas of gravity and acceleration. More specifically, Einstein realised that there was an equivalence between uniform acceleration and the gravitational field.
Figure 1a shows an astronaut and a newton meter N in a spacecraft. The spacecraft is in deep space, extremely far from any other masses, and its engines are switched off, so it (and all its contents) has an acceleration a = 0 m s–2. The display on the newton meter shows a reading of 0.00 N.
Figure 1a
The engines are switched on such that the spacecraft is given an acceleration a = 5 m s–2 as shown in Figure 1b. As a result, the display on the newton meter shows a reading of 300.00 N.
Figure 1b
(i) Interpret the readings on the newton meter N in Figure 1a and Figure 1b.
The astronaut in Figure 1b is holding a tennis ball in hand 1.40 m above the ground of the spacecraft and lets it go at a time t = 0 s.
Describe and explain the subsequent motion of the tennis ball from the perspective of the astronaut.
Include any relevant calculations in your answer.
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