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Two forces F1 and F2 act on a particle. F1 has magnitude 6N and in direction 45°, and F2 has magnitude 7N and in direction 154°. Find the magnitude and direction of their resultant
A wheel is accelerated from rest to 30 rad/s by torque of 200 Nm. The wheel turns
through 20 radians during this time.
Calculate the:
i. Angular acceleration
10. Table 2.6 shows values of the displacement and velocity of a falling object. Copy and complete the table, and use it to draw displacement–time and velocity–time graphs for the object. (Take g = 10 m/s2 .) Table 2.6 The motion of a falling object – see Question 10 Time t (s) 0 1 2 3 4 Displacement s (m) 0 5 20 Velocity v (m/s) 0 10 20
4 A uniform girder, of weight 14 kN and of length 8.0 m, rests horizontally on two wooden blocks, one at 1.0m from one end of the girder and the other at 0.5 m from the other end (as shown below). Calculate the force of the girder on each block.
A car, of weight 6.2 kN, is towed at constant speed by a van on an uphill road as shown below. The tow rope is at an angle of 15° above the horizontal, when the road is 5° above the horizontal. The tension in the tow rope pulls the car with a force of 580 N.
a Calculate the component of the tension in the tow rope:
i parallel to the road, ii perpendicular to the road.
b Calculate the component of the car's weight:
i parallel to the road,
ii perpendicular to the road.
c By comparing your answers to parts ai and bi, calculate the magnitude and direction of the force of friction acting on the car.
d The van's weight is 12 kN. By considering the component of the van's weight parallel to the road and the component of the tension in the tow rope, show that the force of the van's engine must be at least 1.6 kN.
A yacht is moving due North as a result of a force, due to
the wind, of 350N in a horizontal direction of 40° East of
due North, as shown below.
Calculate the component of the force of the wind:
i) in the direction in which yacht is moving,
ii) perpendicular to the direction in which the yacht is moving.
1 A tug boat is used to pull a barge along a river at constant velocity, as shown below. The tug boat pulls on the barge with a force of 4.5 kN. The tug-boat engine drives the tug boat forward with a force of 7.0 kN.
Calculate:
The drag force on the boat due to the water,
The drag force on the barge due to the water.
- Two small silver spheres each with a mass of 100gm are separated by 1 m. Calculate the number of electrons that must be transferred from one to the other to produce an attractive force of 104 N between the spheres.
A sample of air has a temperature of 40.0◦C and occupies a volume of 2.30ℓ. At what temperature would it occupy a volume of 6.50ℓ?
A steel bridge is 625m long when the temperature is 0◦C. If the bridge did not have any expansion joints, how much longer would the bridge be on a hot summer day when the temperature is 35◦C? (Use the linear co¨efficient of expansion for iron.)
