4.3 Mechanics and Materials - Motion along a straight line 1 Questions

4.3 Mechanics and Materials - Motion along a straight line 1 – Questions

Q1.

Spectacle lenses can be tested by dropping a small steel ball onto the lens, as shown in the figure below, and then checking the lens for damage.

A test requires the following specifications:

diameter of ball = 16 mm mass of ball = 16 g height of drop = 1.27 m

(a) Calculate the density of the steel used for the ball.

density = ____________________kg m–3

(3)

(b) In a test the ball bounced back to a height of 0.85 m. Calculate the speed of the ball just before impact.

speed = ____________________m s–1

(2)

(c) Calculate the speed of the ball just after impact.

speed = m ____________________m s–1

(2)

(d) Calculate the change in momentum of the ball due to the impact.

momentum = m ____________________ kg m s–1

(2)

(e) The time of contact was 40 ms. Calculate the average force of the ball on the lens during the impact.

average force = ____________________ N

(2)

(f) Explain, with reference to momentum, why the test should also specify the material of the plinth the lens sits on.

___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (2) (Total 13 marks)

Q2.

A lunar landing module is descending to the Moon’s surface at a steady velocity of 10.0 m s–1_{. At a height of 120 m a small object falls from its landing gear. Assuming that the}

Moon’s gravitational acceleration is 1.60 m s–2_{, at what speed, in m s}–1 _{does the object}

strike the Moon?

A 22.0 B 19.6 C 16.8

D 10.0

(Total 1 mark)

Q3.

A perfectly elastic rubber ball falls vertically from rest and rebounds from the floor. Which one of the following velocity-time,

v–t

, graphs best represents the motion from the

moment of release to the top of the first rebound?

(Total 1 mark)

Q4.

(a) Explain why a particle is accelerating even when it is moving with a uniform speed in a circular path.

___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________

(2)

(b) Figure 1 shows a schematic diagram of a proton synchrotron. This is a device for accelerating protons to high speeds in a horizontal circular path.

Figure 1

In the synchrotron the protons of mass 1.7 × 10–27 _{kg are injected at point A at a}

(i) Show on Figure 1 the direction of the force required to make a proton move in the circular path when the proton is at the position marked P.

(1)

(ii) Calculate the force that has to be provided to produce the circular path when the speed of a proton is 8.0 × 106 _{m s}–1_.

(2)

(iii) Sketch on Figure 2 a graph to show how this force will have to change as the speed of the proton increases over the range shown on the

x

-axis. Insert an appropriate scale on the force axis.

Figure 2

(c) Before reaching their final energy the protons in the synchrotron in part (b) travel around the accelerator 420 000 times in 2.0 s.

acceleration of free fall,

g

= 9.8 m s–2

(i) Calculate the total distance travelled by a proton in the 2.0 s time interval.

(2)

(ii) Unless a vertical force is applied the protons wold fall as they move through the horizontal channel.

Calculate the distance a proton would fall in two seconds.

(2)

(iii) Determine the force necessary to prevent the vertical movement.

(1) (Total 12 marks)

Q5.

A car accelerates at a steady rate of 2.5 m s–2 _{along a straight, level road. The mass of}

(a) Calculate the magnitude of the resultant force acting on the car.

___________________________________________________________________ ___________________________________________________________________

(2)

(b) When the accelerating car reaches a speed of 2.2 m s–1_{, the total force opposing}

the motion of the car is 410 N. Calculate

(i) the driving force provided by the wheels,

______________________________________________________________ ______________________________________________________________ (ii) the power delivered to the wheels of the car.

______________________________________________________________ ______________________________________________________________

(3)

(c) Explain how the total force opposing the motion of the car is affected when it is travelling up a hill. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (1) (Total 6 marks)

Q6.

The figure below shows a motorcycle and rider. The motorcycle is in contact with the road at A and B.

The motorcycle has a weight of 1100 N and the rider’s weight is 780 N. (a) State the Principle of Moments.

___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________

(2)

(b) Calculate the moment of the rider’s weight about B. Give an appropriate unit.

answer = ______________________

(2)

(c) By taking the moments about B, calculate the vertical force that the road exerts on the front tyre at A. State your answer to an appropriate number of significant figures.

answer = ______________________ N

(4)

(d) Calculate the vertical force that the road exerts on the rear tyre at B.

answer = ______________________ N

(1)

(e) The maximum power of the motorcycle is 7.5 kW and it has a maximum speed of 26 m s–1_{, when travelling on a level road.}

Calculate the total horizontal resistive force for this speed. answer = ______________________ N (2) (Total 11 marks)

Q7.

(a) (i) Explain what is meant by the spring constant k of a spring.

______________________________________________________________ (ii) Give the unit of k.

______________________________________________________________

(2)

In bungee jumping, the participant jumps from a high point attached to an elastic cord

(step 1). After a period of free fall, the cord slows the fall of the jumper (step 2) with the system eventually undergoing oscillation (step 3).

A bungee jump is to be set up from a suspension bridge with the jumper of weight 700 N falling towards the river below. The roadway of the bridge is 76 m above the river surface. The bungee cord is adjusted so that the jumper just reaches the river surface at the bottom of the first oscillation.

The unstretched length of the elastic cord is to be 12 m.

(i) Calculate the time taken before the cord begins to stretch.

(ii) Show that, when jumping from the bridge to the river, the jumper loses about 53 kJ of gravitational potential energy.

(iii) Calculate the extension of the cord when the jumper is at the bottom of the first oscillation.

(iv) The gravitational potential energy is stored in the bungee cord. Calculate the spring constant of the cord.

(v) Calculate the time period of oscillation of the jumper.

(12)

(c) (i) Calculate the tension in the cord when the jumper comes to rest for the first time.

(ii) Forces on astronauts and ‘thrill seekers’ are often specified in terms of the g force acting on the participants.

1g is equivalent to an acceleration of 9.8 m s−2.

Calculate the maximum g force that acts on the jumper.

(iii) Hardened thrill seekers prefer their sports to generate 3g or more. Without carrying out detailed calculations, suggest the changes that would need to be made to the cord in order to produce a greater g force for the 700 N jumper. ______________________________________________________________

______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ (6) (Total 20 marks)

Q8.

Galileo used an inclined plane, similar to the one shown in the figure below, to investigate the motion of falling objects.

(a) Explain why using an inclined plane rather than free fall would produce data which is valid when investigating the motion of a falling object.

___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________

(2)

(b) In a demonstration of Galileo’s investigation, the number of swings of a pendulum was used to time a trolley after it was released from rest. A block was positioned to mark the distance that the trolley had travelled after a chosen whole number of swings.

See the figure below.

The mass of the trolley in the figure above is 0.20 kg and the slope is at an angle of 1·8º to the horizontal.

(2)

(ii) Calculate the initial acceleration down the slope. answer = ______________________ m s–2 (2)

(c) In this experiment, the following data was obtained. A graph of the data is shown below it.

time / pendulum swings distance travelled /m

1 0.29

2 1.22

3 2.70

From the graph above, state what you would conclude about the motion of the trolley?

Give a reason for your answer.

___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________

(2)

(d) Each complete pendulum swing had a period of 1.4 s. Use the graph above to find the speed of the trolley after it had travelled 3.0 m.

answer = ______________________ m s–1 (3) (Total 11 marks)

Q9.

(a) A parcel of mass 15 kg drops from a delivery chute onto a conveyor belt as shown in Figure 1.

The belt is moving at a steady speed of 1.7 m s−1.

The parcel lands on the moving belt with negligible speed and initially starts to slip. It takes 0.82 s for the parcel to gain enough speed to stop slipping and move at the same speed as the conveyor belt.

Figure 1

(i) Calculate the change in kinetic energy of the parcel during the first 0.82 s.

change in kinetic energy ____________________ J

(2)

(ii) The average horizontal force acting on the parcel during the first 0.82 s is 31 N.

Calculate the horizontal distance between the parcel and the end of the delivery chute 0.82 s after the parcel lands on the conveyor belt. Assume that the parcel does not reach the end of the conveyor belt.

horizontal distance ____________________ m

(2)

(b) At a later stage the parcel is being raised by another conveyor belt as shown in

Figure 2.

Figure 2

This conveyor belt is angled at 18° to the horizontal and the parcel moves at a steady speed of 1.7 m s−1 without slipping.

Calculate the rate at which work is done on the parcel.

rate at which work is done ____________________ W

(3) (Total 7 marks)

Q10.

Take the acceleration due to gravity,

g

E, as 10 ms−2 on the surface of the Earth.

The acceleration due to gravity on the surface of the Moon is . An object whose weight on

Earth is 5.0 N is dropped from rest above the Moon’s surface. What is its momentum after falling for 3.0s? A 2.5 kg m s−1 B 6.2 kg m s−1 C 15 kg m s−1 D 25 kg m s−1 (Total 1 mark)

Q11.

A mass of 2.5 kg is released from rest at X and slides down a ramp, of height 3.0 m, to point Y as shown.

When the mass reaches Y at the bottom of the ramp it has a velocity of 5.0 m s–1_.

What is the average frictional force between the mass and the ramp? A 8.5 N B 10.6 N C 14.7 N D 24.5 N (Total 1 mark)

Q12.

The diagram shows a strobe photograph of a mark on a trolley X, moving from right to left, in collision with another trolley Y which had no mark on it.

After the collision both trolleys are in motion together.

Which one of the following is consistent with the photograph?

A Trolley Y has the same mass as trolley X and was initially stationary B Trolley Y had a smaller mass than X and was moving from right to left

C Trolley Y had the same mass and was initially moving left to right at the same speed

as trolley X

D Trolley Y had the same mass and was initially moving left to right at a higher speed

than trolley X

(Total 1 mark)

Q13.

The velocity of a vehicle varies with time as shown by the following graph.

Which graph below represents how the resultant force

F

on the car varies during the same time? A B C D A B C

D

(Total 1 mark)

Q14.

A steel ball of weight

W

falls through oil. At a time before the ball reaches terminal velocity, the magnitude of the viscous resistance force on the ball is

A zero

B between zero and

W

C equal to

W

D greater than

W

(Total 1 mark)

Q15.

A body is accelerated from rest by a constant force.

Which one of the following graphs best represents the variation of the body’s momentum

p

with time

t

?

(Total 1 mark)

Q16.

A roller coaster car is raised to a height of 65 m and released from rest. What is the maximum possible speed of the car?

B 25 m s−1

C 36 m s−1

D 130 m s−1

(Total 1 mark)

Q17.

The graph shows how the force acting on a body changes with time.

The body has a mass of 0.25 kg and is initially at rest. What is the speed of the body after 40 s assuming no other forces are acting?

A 200 ms–1 B 400 ms–1 C 800 ms–1 D 1600 ms–1 (Total 1 mark)

Q18.

A girl jogs at 2.0 m s–1 _{in a straight line for 30 seconds, turns around and returns to her}

starting point 20 seconds later.

What is her average velocity and average speed?

Average velocity/m s–1 _{Average speed/m s}–1

A 0 m s−1 2.4 m s−1

C 1.0 m s−1 2.0 m s−1

D 2.5 m s−1 2.5 m s−1

(Total 1 mark)

Q19.

A car accelerates uniformly from rest along a straight road. Which graph shows the variation of displacement x of the car with time t?

A B C D A B C D (Total 1 mark)

Q20.

The velocity–time graph for a falling object is shown.

A B C D (Total 1 mark)

Q21.

A ballbearing

X

of mass 2

m

is projected vertically upwards with speed

u

. A ballbearing

Y

of mass

m

is projected at 30° to the horizontal with speed 2

u

at the same time. Air resistance is negligible. Which of the following statements is correct?

A The horizontal component of

Y

's velocity is

u

.

B The maximum height reached by

Y

is half that reached

by

X

C

_X

and

Y

reach the ground at the same time.

D

_X

reaches the ground first.

(Total 1 mark)

What is the relationship between the distance

y

travelled by an object falling freely from rest and the time

x

the object has been falling?

A

_y

is proportional to

x

2 B

y

is proportional to √

x

C

y

is proportional to D

y

is proportional to (Total 1 mark)

Q23.

A firework is fired vertically up into the air and subsequently falls to the ground.

Which quantity relating to the motion of the rocket is never zero before it hits the ground? Assume that air resistance is negligible.

A acceleration B velocity C momentum D kinetic energy (Total 1 mark)

Q24.

An object is accelerated from rest by a constant force F for a time t. Which graphs represent the variation of time with the change in the kinetic energy and the change in momentum of the object?

Kinetic energy Momentum

A

C D A B C D (Total 1 mark)

Q25.

Which row gives two features of graphs that provide the same information?

Feature 1 Feature 2

A Gradient of a

displacement–time graph

Area under a velocity–time graph B Gradient of a displacement–time graph Area under an acceleration–time graph C Gradient of a velocity–time graph Area under a displacement–time graph D Gradient of a velocity–time graph Area under an acceleration–time graph (Total 1 mark)

Q26.

An object is dropped from a cliff. How far does the object fall in the third second? Assume that g = 10 m s–2_. A 10 m B 20 m C 25 m D 45 m (Total 1 mark)

Q27.

A body travels with speed v, which varies with time t as shown in the graph.

Which one of the graphs, A to D, shows how the distance s covered by the body varies with time t? A B C D (Total 1 mark)

Q28.

Which graph best represents the velocity–time graph for a ball that is dropped from rest and bounces repeatedly?

A B C D (Total 1 mark)