# physics maths

1. The sides of a cuboid are measured to 3,202 cm; 0.0012 cm and 11.2 cm respectively. Calculate the volume of the cuboid and write down with the correct number of value digits.

Volume of the cuboid equals 3202 0.0012 11.2 = 43.03 cm3

• A 9.2 dm long and evenly thick rod rests on a support. 0.55 dm from one end is hung a dynamometer so that the bar will hang horizontally. Then the dynamometer shows 4.4 N. How much does the bar weigh?

Weight of the bar is gotten by:  L1M1 = L2M2

2.1 dm weight of the bar(x) = 3.05dm 4.4N

0.21m xN = 0.305m 4.4N

xN = 63.90 N

• A rod AB which is homogeneous and even in thickness has a length of 2.70 m and is rotatable about an axis at A. The rod weighs 25 kg and is held in equilibrium by a force F which has its point of attack in B. The angle between the direction of the force and the rod is 45 degrees. How big is the force F?

Forces are equilibrium accounts for M1L1 = M2L2

25kg 1.35m = F 2.7m

4.183 N 1.35m = F 2.7m

But F is at 45o

4.183 N 1.35m = F Cos 45 2.7m

2.092 =0.5253F

F =3.982N

• A carriage rolls at a constant speed to the right. On the cart is an upward cannon that suddenly shoots a bullet away. The carriage continues to the right at the same speed as before. Where does the ball end when it falls down? For a detailed reasoning.

Once the bullet is fired, it will speed away at its speed plus that of the carriage. Therefore, the ball end of the bullet will fall away from the shooting point whether the carriage continues at same speed or remains stationary.

• A river is 200 m wide. The water in the river flows at a speed of 2.5 m / s. A motorboat travels across the river at its maximum speed which in stagnant water is 5.0 m / s. The boat is always heading perpendicular to the river’s beaches. Where does the motor boat land on the other beach?

The relative speed of the boat will be = 5.385m/s

The angular drift by water is tan 5.385 div 2 = 1.216

Hence, boat will reach the bank at 1.216 meters down stream

• A ball of mass 2.0 hg moves at a constant speed in a circular path. The radius of the track is 1.5 m and it takes the ball 3.0 seconds to move one lap. How big is the centripetal force?

Force = mass * centripetal acceptation

Acceleration = 0.3142m/s2

Force =2m * 0.3142m/s= 0.6283N

• A ball moves at constant speed. Can we then safely say that the result of the forces acting on the ball is zero? Motivate and discuss your answer.

Yes, the result of the force acting on the ball is zero. It is able to counter the effect of gravity and friction that would slow the ball. By Newton laws of motion

• A conductor is in the middle of the poles on a permanent magnet. The current in the conductor moves in the direction towards the paper plane (away from the reader). How is the force acting on the conductor directed?

a) To the right of the figure

b) To the left of the figure

c) Down in the figure

d) Upwards in the figure

• Protons come in horizontally from the left between two large metal plates at the velocity v = 0.80 mm / s. The plates are connected to a voltage source with pole voltage U. Between the plates is a homogeneous magnetic field with the flow density 38 mT directed perpendicular to the plane of the paper. The distance between the plates is 1.5 cm. They want the protons to continue with unchanged direction and speed between the plates. Which of the plates should be connected to the positive pole of the voltage source and how large should the voltage U be?

The top plate should be connected to a voltage higher than 0.80

1. The magnetic flux Φ through a 700-turn coil decreases linearly with time as shown in the diagram below. Calculate the voltage across the coil at time t = 1.0 ms.

300 volts

1. The current in a coil with the inductance 35 mH has at a certain moment the growth rate 6.2 A / s. What is the instantaneous value of the ems induced in the coil?

5.5 mH