Exercise

Lift

1.Subra stands on a weighing machine in a lift. If the mass of Subra is 58 kg, determine the reading of the weighing machine when the lift is.

(a)stationary

(b)moving upward with a uniform velocity of 2 ms-1

(c)moving upward with a uniform acceleration of 1 ms-2

(d)moving downward with a uniform acceleration of 1 ms-2

(consider gravitational acceleration, g to be 10 ms-2)

2.A box of mass 1.6 kg is suspended from a spring balance hanging from the ceiling of a lift.

What is the reading on the spring balance if

(a)the lift is stationary?

(b)the lift moves upwards at an acceleration of

2 ms-2?

(c)the lift moves downwards at an acceleration of

3 ms-2?

Pulley System

1.Two masses of 5 kg and 3 kg are connected to a rope which passes over a frictionless pulley.

Find the tension in the rope and the acceleration of the 3 kg mass when the 5 kg mass is released.

2.A 1.5 kg trolley is being pulled by a 0.5 kg weight with the help of a pulley system.

Calculate the acceleration of the trolley.

(Take g = 10 ms-2)

3.Figure shows a pulley system with two loads, A and B, connected by a non-elastic rope that passes over a frictionless pulley. (Take g = 10 ms-2)

(a)Determine the resultant force, F, of the system and state the direction of the movement of each load.

(b)Calculate the magnitude of the acceleration of load A.

4.A 2 kg weight is connected by a rope to a 3 kg wooden block. The rope passes over a smooth pulley as shown in figure.

The weight is then released. Find the tension in the rope if a friction of 5 N acts against the wooden block.

Force In Equilibrium

Resultant Force

1.An ocean liner is towed into harbour by two tugs, A and B, exerting forces of 12 kN and 10 kN respectively and the tow ropes making an angle 68. Find the resultant force acting on the liner.

2.Figure shows a boat being pulled by two forces with a magnitude of 300 N and 400 N respectively. The angle between the forces is 60.

Determine the magnitude and the direction of the resultant force using the parallelogram of forces method.

3.Samy and Heng pull a crate with forces 70 N and 90 N respectively.

Find the resultant force on the crate due to these two forces.

4.Two forces of magnitude 5N and 12 N act at a point respectively as shown I figure below. The forces are perpendicular to each other.

Resolution of Forces

1.Find the horizontal and vertical components for each of the following forces.

2.A boy is pulling a toy car with a force of 6 N as shown in figure.

Find the horizontal component of the force. If the toy car is moving with constant velocity. What is the friction against the toy car?

3.Santhiran pulls a 5 kg crate on the floor with a force of 35 N. The friction against the box is 8N.

What is the acceleration of the crate?

4.A gardener pushes a 250 kg concrete roller with a force of 200 N directed from the handle. The handle is at an angle of 33 to the horizontal.

(a) Find the horizontal and vertical components of the force.

(b)What is the weight of the concrete roller?

(c)If the gardener pulls the handle with the same force in a reverse direction, what is the downward force on the ground then?

(d)In which direction, pushing or pulling, would the roller be more effective in levelling the grass?

5.Eric and Darren are pulling a trolley on which their sister, Tina is sitting. Both Eric and Darren pull the rope with a force of 50 N, which makes an angle of 30 with the direction of motion.

The total mass of Tina and the trolley is 30 kg and the friction between the trolley and the floor is 40 N.

What is

(a)the total of forces towards the left?

(b)the acceleration of Tina and the trolley?

6.Find the resultant force of the two forces as shown in figure.

Three Forces In Equilibrium

1.

A carton of mass 5 kg is at rest on an inclined plane making an angle of 15 with the horizontal. Find the frictional force and the normal reaction force acting on the carton.

2

Figure shows a horizontal force, F acts on a wooden block of weight 8 N placed on a smooth plane inclined at 30 to the horizontal.

What must the magnitude of F be to prevent the block from sliding down?

3.

Joan and her sister lift a pail of water of total mass 5.6 kg. Each of them exerts a force of F at 25 to the vertical. Find the magnitude of F.

4.

A lamp of weight 25 N is supported by two ropes as shown in figure.

Given that the tension in rope A is 20 N, find

(a) the angle of ,

(b) the tension in the rope B

5.

Each elephant in the diagram is pilling a rope attached to a mass of 10 kg. The elephants pull with a force of 5000 N.

Find the angle between the ropes

Can the ropes be pulled to become horizontal?

6.

A mirror of weight 12 N is hung on the wall using a string as shown.

Draw a scale drawing of a triangle of forces to determine the tension, T in the string.

(use the scale 1 cm : 2N)

7.Two forces of 60 N and 80 N act on an object.

Find

(a) the greatest and the smallest forces that can be exerted.

(b) the resultant force if the force 80 N is acting to the right and is at right angles to the 60 N force.

(c) the resultant force if the force 80 N is acting to the right and is at 120 to the 60 N force.

8.

Two astronauts push a 800 kg satellite with forces of 35 N and 45 N which make an angle of 60 with each other. Find the resultant force and the acceleration acquired by the satellite.

9.

Aunty Anne is ironing with a force of 6 N as shown.

What is the effective force that pushes the iron forwards.

10.

In a circus, a monkey is pulling his chain with a forward force of 20 N as shown.

What force does the clown need to apply to the chain to prevent the monkey from moving forward?

11.

A footballer is injured and requires traction on his foot as shown.

In the force of the traction is 125 N, what is the mass, m required to pull the rope?

12.

A boy exerted a force of F to pull a box of mass 2 kg up an inclined plane which makes an angle of 30 with the floor.

Given that the friction acting on the box is 3 N, find

(a) the normal reaction force, R acting on the box,

(b) the component of the weight down the plane,

(c) the value of F is the box is moving up the plane with an acceleration of 1 ms-2

13.

A 3.5 kg flowerpot is supported by two ropes as shown.

The rope attached to the wall is horizontal and the rope attached to the ceiling makes an angle of 30 with the horizontal.

Find the tension in each rope.

14.

A wooden block is placed on top of a smooth runway of length 2 m. The angle of inclination with the floor is 30. Find

(a) the time and

(b) the velocity of the block

When it reaches the bottom of the runway.

15.A bird of mass 0.6 kg stands on the midpoint of a horizontal rope. The rope sags and an angle of 150 is formed.

Find the tension in the rope

16. A traffic light of mass 15 kg is suspended from two cables as shown.

Find the tension in each cable.

17.(a) Explain the equilibrium of forces.

(b) Figure shows a ball resting on a field.

Draw and label the two forces that cause the ball to be at rest.

(c) Figure shows a picture frame being held by two identical strings.

Draw and label the three forces that are in equilibrium so that the frame is at rest.

18.(a) What is meant by resultant force?

(b) Figure shows forces acting on three objects.

In each of the objects, determine the magnitude and direction of the resultant force

19Two boats, P and Q are used to pull a raft carrying a few elephants. Boat P uses a force of 4500 N in the direction of 30 NW. Boat Q uses a force of 5000 N in the direction of 20NE.

(a) calculate the magnitude of the resultant force.

(b) determine the direction in which the raft is moving

20.A conductor uses a scraper to scrape old paint away from a wall. He uses a force of 12 N at an angle of 36 with the wall.

Calculate

(a)the vertical

(b)the horizontal

Components of the force acting on the wall.

21During a training session, a 50 kg trainee is at rest by holding two identical ropes, each at an angle of 40with the vertical.

(a)What is the weight of the trainee?

(b)Calculate the tension of each rope

(g = 9.8 Nkg-1)