Further Mechanics
A footballer kicks a football from the penalty spot. A graph of force on the ball against time is drawn. The area under the force-time graph represents
change in momentum or impulse
A 520 microfarad capacitor is charged so that the potential difference across it increases at a constant rate from 0 V to 4.5 V in 25 s. The current that is charging the capacitor is
94 micro ampere / 94 x10-6 A
The unit of magnetic flux density is the tesla T. The unit T could also be written,in terms of N, A and m, as
N A-1 m-1
In the particle accelerator called the Linac, the particles gain kinetic energy because
they are accelerated by an electric field.
The spinning top has a diameter of 22 cm and spins at a rate of 6.5 revolutions per second. The speed of a point on the outer edge of the spinning top is
4.5 m s-1
Two small point charges are separated by a short distance as shown in the diagram. Calculate the resultant electric field strength at B, a distance of 0.33 m from each charge.
0.043 N C-1
The graph shows how the flux linkage through a coil varies with time. The e.m.f. induced in the coil over the same period of time
is constant and then becomes zero.
Particle detectors often use magnetic fields to deflect particles so that properties of the particles can be measured. A moving charged particle of mass m, charge q and velocity v enters a uniform magnetic field of flux density B.
a) State the charge on the particle.
b) Describe and explain the shape of the particle’s path in the magnetic field.
a) negative
b) circular path because the force is always perpendicular to the motion of the particle
A student holds a piece of string with a small spherical mass attached to the other end. She rotates the mass at a constant angular velocity, in a vertical circular path. The string has a length of 25.0 cm and is attached to a mass of 204 g. It is rotated in a vertical circle with the string remaining taut at all times. When the mass is at the top of the circle it is moving with an angular velocity of 9.90 rad s–1. Calculate the tension in the string at this position.
3.0 N
The graph shows how the resultant electric field strength ER varies with distance along the horizontal axis from point A. A maximum occurs at point C. The electric field strength at C is 0.044 N C–1. A positive ion enters the electric field travelling along the axis towards the right. The ion has a speed of 1500 m s–1 at point A. Calculate the maximum acceleration of the ion as it passes through the field.
mass of ion = 6.6 x10-27 kg
charge on ion = 3.2 x10-19 C
2.1 × 106 m s−2
An alpha particle moves at right angles to a uniform magnetic field and experiences a force F. A beta particle moves at right angles to a magnetic field of half the magnetic flux density but at ten times the velocity of the alpha particle. The magnitude of the force, in terms of F, on the beta particle will be
2.5 F
An electron has a momentum of 1.9 x10-24 kg m s-1. The kinetic energy of the electron is
2.0 x10-18 J
The diagram shows a car of mass 950 kg at the highest point X of the bridge. The bridge forms part of a vertical circle of radius 20.0 m. Calculate the total upward force R of the road on the car when the car is passing point X at a speed of 12.0 m s-1.
2480 N
A student sets up the circuit as shown in the diagram. She moves the switch S from X to Y. The student wants to use this circuit to produce a short time delay of 0.20 s after the switch moves from X to Y. Calculate the value of the potential difference across the capacitor after this time interval.
0.13 V
A current of 1.50 A flows in a straight wire of length 0.450 m. The wire is placed in a uniform magnetic field of flux density 2.00 × 10–3 T which acts perpendicular to the wire. Under these conditions the magnetic force balances the weight of the wire. Calculate the mass of the wire.
1.38 x10-4 kg
A mass-spectrometer is an instrument that is used to measure the masses of molecules. Molecules of a gas are ionised and travel through a vacuum in a narrow tube. The ions enter a region of uniform magnetic flux density B where they are deflected in a semicircular path as shown in the diagram. The ions have a charge of +e and a speed of 1.20 x105 ms-1.Calculate the mass of an ion.
6.64 x10-26 kg
In a bowling game, a player rolls a small ball along the ground. The diagram shows the action of the player as he starts to swing his arm forward at A, to the point when the ball is rolling along the ground at C. The player exerts a forward force on the ball between A and B. The ball rolls along the ground until it collides with a stationary ball of mass 1.2 kg. After the collision both balls roll off at an angle to the original direction of the moving ball as shown in the diagrams.
After the collision:
- the 1.5 kg ball travels at 0.7 m s-1 at an angle of 45o to its original direction
- the 1.2 kg ball travels at 1.8 m s-1 at an angle of 20o to the original direction of the moving ball.
Calculate the velocity of the first ball as it collides with the second ball.
1.8 m s-1
Two point charges Q1 and Q2 are placed 20 cm apart. Q1 has a charge of +3.0 microcoulomb and Q2 has a charge of +6.5 microcoulomb. At point P, a distance 8.1 cm from Q1, the electric field is about
2000 N C-1
A student is investigating electromagnetic induction using a U-shaped magnet. The magnetic flux density between the poles of the magnet is 74 mT. The magnetic field outside the region of the poles is negligible. She places a stiff copper wire between the poles of the magnet as shown in the diagram. The wire is connected to an ammeter of resistance 0.25 ohms. The rectangular poles measure 6.0 cm x 2.4 cm. Calculate the magnetic flux between the poles of the magnet.
1.1 x10-4 Wb
Accelerators are used to collide high energy particles so that their interactions can be studied. Which quantity is not always conserved in an interaction between particles?
rest mass