Forces & Momentum (HL IB Physics)

A wooden block of weight W rests on a rough board that produces a friction force F_f. The end of the board is then raised up to angle θ until the block slides down the plane of the board at constant velocity v.

Which row describes the forces acting on the block as it slides down the board?

Which row gives the correct Newton’s third law force pair for a book on a table?

An object of mass m is connected via a frictionless pulley to an object of mass M, where M > m. M rests on a horizontal rough surface with a frictional force f.

What is the acceleration of the system?

A photo hangs from two strings. It has a weight W and the two strings have equal tension T.

What is the free–body diagram for this situation?

Which of the following are possible values for the maximum coefficient of static friction,  and dynamic friction, ?

A.	0.012	0.78
B.	0.35	0.12
C.	1.50	0.90
D.	0.26	–0.77

Two coplanar forces of 11 N and 7 N act on an object. Which force could not be the resultant for these two forces?

Two boxes in contact are pushed in a line along a floor with a force F. The boxes are moving at a constant speed. Box X has a mass m and box Y has a mass 3m.

What is the resultant force acting on Y?

A particle of mass m moves in a circle of radius r at uniform speed, taking time T for each revolution. What is the kinetic energy of the particle?

A 0.05 kg ball is attached to an inextensible string and whirled overhead such that it rotates in a horizontal circle.

What is the centripetal force on the ball if the string is 0.1 m long and the ball has a time period of  s?

A horizontal disc rotates uniformly at a constant angular velocity about a central axis normal to the plane of the disc.

Point X is on a distance 3L from the centre of the disc. Point Y is a distance L from the centre of the disc. Point Y has a linear speed v and a centripetal acceleration a.

What is the linear speed and centripetal acceleration of point X?

A spinning top makes twenty revolutions in five minutes in a clockwise direction.

What is the angular velocity of the spinning top?

A body moves in a circle with increasing angular velocity. At times t, the angles θ swept out by the body added cumulatively from the same reference point and its angular velocities ω are as follows:

The angular acceleration of the body:

A hammer thrower rotates a ball on a string in a circular path gradually increasing its angular velocity with each rotation. 

When the hammer releases the ball, the subsequent path taken by the ball is

An object at the end of a steel rod rotates in a vertical circle at a constant angular velocity. Which of the following statements correctly describes the tension in the rod?

For a particle moving in a circle with uniform speed, which of the following statements is incorrect?

A satellite X of mass orbits the Earth with a period T and radius r and linear speed v. What will be the orbital period of satellite Y with mass m occupying an orbit with radius  and speed 2v as X?

A force acts on a mass of 5.0 kg and it is initially at rest.

What is the time taken for the mass to reach an acceleration of 2 m s^-2?

A body of mass 3M at rest explodes into two pieces of mass 2M and M. 

What is the ratio  and ?

A.		-1
B.	1	-1
C.		2
D.		-2

Which of the following is an elastic collision?

A stone of mass 0.5 kg is thrown with an initial speed of 10 m s^-1 at an angle θ to the vertical. P is the highest point of the motion and air resistance is negligible.

What is the momentum of the stone at P?

A truck T moving horizontally collides with an identical truck S that is at rest.

 T strikes S with speed 2v.

What is a possible outcome of the collision?

A ball of mass 4.0 kg, initially at rest, is acted on by a force F which varies with t.

What is the velocity of the ball after 14 s?

Which of the following is true for momentum and impulse?

Two balls m and 2m collide elastically with speeds v and 2v respectively. After the collision, they both move in opposite directions.

What speed does the 2m ball move with after the collision?

A frictionless spring-operated latched is fitted to a door. 

When the latch is pushed in, the spring compresses.

When the latch is released, which of the following best represents how acceleration a of the latch varies with the distance x it moves before stopping? 

Elaborate chandeliers can be modelled as layers of hanging bars. The diagram shows one such model with a mass m suspended from two bars of negligible mass, connected by five light strings. Each layer has N number of strings. 

Which expression gives the tension in any single string? 

Two blocks, one made of wood and the other of iron, are arranged at rest on the ground. 

Which of the following statements is correct? 

A pendulum bob hangs from the ceiling in a carriage in a train and is just above a certain mark on the floor when the train is at rest. Later, when the train is moving with a constant velocity forward, which statement best outlines the position of the bob? 

Two masses m and nm, where n > 1, are joined by a light string which passes over a frictionless pulley. The acceleration of free fall is g. 

What is the acceleration of the masses a and the tension in the string T? 

Two bodies, X and Y, having masses m_X and m_Y respectively, exert forces on each other and have no external forces acting on them. The force acting on X is F, which gives X an acceleration a_X.

What is the magnitude of the force on Y and its acceleration?

Two blocks with mass 5m and 3m are pushed along a smooth horizontal surface by an applied force F.

What is the magnitude of the force exerted between the blocks? 

A particle rotates clockwise in a horizontal circle of radius r with a constant angular velocity ω. The particle is at S at time zero and at P at time t. Q represents the projection of point P onto the diameter through S. Measured with respect to the centre of orbit O, the displacement, linear velocity and linear acceleration of Q along OS are x, v and a respectively. 

Which of the following sets of expressions is correct? 

		v	a
A.
B.
C.
D.

A simple pendulum consists of a bob of mass m at the end of a light inextensible thread of length d. The bob swings through point Y with velocity v and comes to an instantaneous rest at point X, where the string is just taut. 

What is the tension in the thread as the bob passes point Y? 

A particle travels in a circular path in a magnetic field with radius x and centripetal acceleration a. 

What is the time taken for 15 complete rotations? 

A mass m₁ is attached to one end of a light extensible string of length x. When the mass rotates with a linear speed v in a horizontal plane, an extension Δx is obtained. 

Which of the following shows the correct expression for another mass m₂, if it is attached to the same light extensible string and rotated with the same linear speed v but rotates at twice the radius as that produced by m₁?

Two bobs A and B, of equal mass, are connected by a light inextensible string of length l. 

Bob A is tied to a nail at the centre of a smooth table by another light, inextensible string of length 3l. The bobs are then set into uniform motion on the surface of the table with the same angular velocity. 

What is the ratio of the tension in the string connecting bob A and B to that in the string connecting bob A to the nail? 

An aircraft moves in a horizontal plane at a constant linear speed v and makes a turn of radius r. 

Which of the following expressions is true for the tilt angle θ?

You may wish to use the relationship:

The maximum speed for a car to safely move round a corner when the road is dry is 10 m s^–1. The maximum frictional force between the road surface and the wheels of the car is halved when the road is wet. 

What is the maximum safe speed for a car to go round the corner when the road is wet? 

A conker attached to a string is whirled in a vertical circle at constant speed. 

Which of the following correctly shows the variation of the tension T in the string with the angular displacement θ? 

A small object is attached to a string and whirled in a vertical circle at a constant speed. The magnitude of the net force F on the object at the top of the circle is given by:

Where T is the tension in the string, m is the object's mass and g is the acceleration of free fall.

The magnitude of the net force on the object at the bottom of the circle is given by: 

Which of the following statements is correct?

Two masses m₁ and m₂ are fixed on a horizontal circular rotating platform. m₂ is half as massive as m₁ and is fixed at a distance three times as far from the centre as m₁. The net force on m₁ is F₁ and the net force on m₂ is F₂.

Which of the following statements is correct? 

A ball of mass 0.60 kg is kicked off a cliff with a horizontal velocity of 3.0 m s^–1.  It follows the path of a projectile shown below and lands with a velocity of 4.0 m s^–1 at an angle of 30^o to the ground.  Air resistance is negligible during the flight.

What is the magnitude of the change in momentum of the ball between the top of the cliff and the ground below?

You may need to use the following trigonometric values to help you:

cos(30) = 

sin(30) = 

A BB gun fires 4 g ball bearings at a rate of 100 balls per minute. The balls leave the BB gun at a velocity of 20 m s^–1 and strike a fixed steel block.  The balls rebound off the block with the same velocity as they were fired.

What is the average force exerted on the steel container?

Two trolleys, X and Y, are connected by an elastic cord, of negligible mass, as shown below. Trolley X is twice the mass of trolley Y.

The two trolleys are pulled apart so that the elastic cord is stretched. The trolleys are then released at the same time and move towards each other.  The trolleys stick together on impact. 

Just before the trolleys collide, the speed of trolley X is 20 cm s^–1.

What is the speed of the trolleys after they collide?

The diagram below shows a block of mass 2 kg sliding down a rough slope from rest against a constant friction force of 2.5 N.

Use the following assumptions to help you:

Acceleration due to free fall is 10 m s⁻²

cos(20) = 0.9

sin(20) = 0.3

What is the momentum of the block along the slope after 5 seconds?

A car of mass 3000 kg is travelling at 5 m s^–1 when it collides with a wall and is brought to rest.  The force-time graph of the impact is shown below.

What is the maximum force exerted on the car?

Particle P has a mass m and is moving towards a stationary particle, Q, of mass M.  P is travelling with a velocity of u before colliding head on with particle Q.  The collision between the particles is elastic.

What is the velocity of particle Q after the collision?