Repetition Exercises, Term 3
Year 9
This document contains examples of exercises that relate to the curriculum in term 3 of year 9.
Accelerated Motion (Equation of Motion):
1) State the definition of velocity and acceleration.
2) A cart in moving at v > 0 and a < 0. What does this mean?
3) A cart in moving at v < 0 and a > 0. What does this mean?
4) A cart in moving at v < 0 and a < 0. What does this mean?
5) A cart in moving at v > 0 and a > 0. What does this mean?
6) A cart in moving at v > 0 and a = 0. What does this mean?
7) A cart in moving at v < 0 and a = 0. What does this mean?
8) What is the difference between speed an velocity?
9) A spaceship is 5000 km from the Moon flying with 500 m/s away from the Moon, when the pilot decides to accelerate. The spaceship accelerates with 10 m/s2 for 7 s getting faster.
a) Calculate the speed of the space ship after having accelerated for 7 s.
b) Calculate the distance to the Moon after 7 seconds.
10) A spaceship is 5000 km from the Moon flying with 200 m/s towards the Moon, when the pilot decides to accelerate. The spaceship accelerates with 10 m/s2 for 7 s getting faster.
a) Calculate the speed of the space ship after having accelerated for 7 s.
b) Calculate the distance to the Moon after 7 seconds. Reason for your sign convention.
Accelerated Motion (Motion Graphs):
11) Consider the motion illustrated below.
a) Calculate the acceleration during the first 10 min.
b) Calculate the acceleration in the time interval between 15 min and 40 min.
c) When is the object at rest?
d) When is the velocity constant?
e) Calculate the total distance covered by the object.
f) Calculate the distance that the object is from its starting point after 55 min.
g) Find sections of the graph that correspond to the situations described in exercises 2-7.
h) Draw the corresponding (t,a)-graph.
i) Draw the corresponding (t,s)-graph.
12) Consider the motion illustrated below. Describe the motion and calculate the total distance covered in the 10 s shown. Furthermore, draw a (t,a)-graph.
Free Fall:
13) A witch falls asleep and falls from her broom 100 m above the ground. Assume free fall – no air resistance.
a) How long does it take before she hits the ground?
b) How fast is she falling after 3 s?
c) How far from the ground is she after 3 s?
d) Draw the corresponding (t,v)-graph for the first 20 s after her fall.
14) You throw your physics book out on the window 50 m above the ground. As always, ignore air resistance.
a) How long does it take before the book hits the ground?
b) How fast is the book falling after 2 s?
c) How long a distance has the book covered after 2 s.
d) How fast is it falling after 5 s?
e) Draw the corresponding (t,s)-graph for the first 10 s after you have thrown the book.
Newton’s Laws of Motion:
15) If you jump out of an airplane, you will reach a terminal speed at some point. This is due to air resistance that increases with your speed. We will take a closer look at this in year 10. But how large does the air resistance have to be for you to stop accelerating? Refer to Newton’s laws.
16) In a popular tale, the Baron of Münchhausen claims to save himself and his horse from drowning by pulling himself up by his hair. Use Newton’s laws to explain, why this story cannot be true.
17) You kick a football with a force of 50 N. The ball is green and has a mass of 500 g. Calculate the acceleration of the ball after you kicked it.
18) Explain the important traits of free body diagrams.
19) Draw a free body diagram of yourself sitting on your chair. What forces are at play?
20) Draw a free force diagram of car acceleration on a horizontal road.
Inclined Planes:
In this term, we have looked at systems that are affected by the force of gravity, and thus we have taken a closer look at the inclined plane. This is, however, just one example of a simple mechanical system, where gravity leads to constant acceleration. Make sure that you understand the principles and derivations, so that you may also apply your knowledge in other situations.
21) A cart with a mass of 1.5 kg rolls down a frictionless plane. The plane has an inclination of 30°.
a) Sketch the situation (keep it simple).
b) Calculate the gravitational force acting on the cart. Include an arrow signifying the force in your sketch.
c) Calculate the component of the gravitational force parallel to the plane. Include an arrow signifying the force in your sketch.
d) Calculate the component of the gravitational force perpendicular to the plane. Include an arrow signifying the force in your sketch.
e) Calculate the acceleration of the cart rolling down the plane.
22) John pushes a wheelbarrow up a ramp – up an inclined plane. The plane has an inclination of 30° and the loaded wheelbarrow has a mass of 40 kg.
a) Sketch the situation and calculate the component of the gravitational force parallel to the plane. Include an arrow signifying the force in your sketch.
b) How much force does John have to apply to push the wheelbarrow up the ramp with constant speed?
c) How much force does John have to apply to push the wheelbarrow up the ramp with an acceleration of 1 m/s2?
23) A mass, m1, of 4 kg is placed on an inclined plane and connected to another mass, m2, of 2 kg via a string. The plane has an inclination of 45°. See the illustration on the next page.
a) Calculate the gravitational force on m2. Include an arrow signifying the force on the illustration above.
b) With what force does m2 affect m1? With what force does m1 affect m2? Include these forces on the illustration above.
c) Calculate the gravitational force on m1 and calculate the component of the gravitational force on m1 parallel to the plane. Include this force on the illustration above.
d) Use the answers from b and c to find the total force on the m1 parallel to the plane.
e) Does m1 slide up or down the plane?
f) Calculate the acceleration of m1 based on the above. Argue for your sign convention.
g) Calculate the change in distance covered by m1 at t = 1 s, if the box starts at rest at t = 0.
24) A mass of 1.2 kg slides down a frictionless inclined plane that has a height, h, of 1.5 m. It starts out at rest at the top.
a) Calculate the potential energy at the top of the plane relative to the ground.
b) Calculate the kinetic energy that a mass has, when the mass reaches them bottom of the frictionless plane.
c) Calculate the velocity corresponding to the kinetic energy found in b.
