Home Learning Quiz - Vector Resolution

1. Two forces of equal magnitude are acting outwards on a point mass. As the angle between the two forces increases from 0^o to 180^o, the resultant force acting on the point mass

Decreases

Increases

Decreases then increases

Increases then decreases

As the angle between the two forces increases from 0o to 180o, the resultant force acting on the point mass decreases. This is because when the forces are acting in the same direction (0o), their magnitudes add up to give a larger resultant force. However, as the angle increases, the forces start to act in opposite directions, causing their magnitudes to cancel each other out. At 180o, the forces are completely opposite and have equal magnitudes, resulting in a net force of zero. Therefore, the resultant force decreases as the angle between the forces increases.

Explanation

As the angle between the two forces increases from 0o to 180o, the resultant force acting on the point mass decreases. This is because when the forces are acting in the same direction (0o), their magnitudes add up to give a larger resultant force. However, as the angle increases, the forces start to act in opposite directions, causing their magnitudes to cancel each other out. At 180o, the forces are completely opposite and have equal magnitudes, resulting in a net force of zero. Therefore, the resultant force decreases as the angle between the forces increases.

2. A horizontal force of 80 N is needed to pull a sled forward. If the rope pulling the sled makes an angle of 30^o with the horizontal, what is the tension in the rope?

40 N

69 N

92 N

160 N

When the rope makes an angle of 30 degrees with the horizontal, the tension in the rope can be calculated using the formula Tension = Force / Cosine(angle). In this case, the force is 80 N and the angle is 30 degrees. Plugging these values into the formula, we get Tension = 80 N / Cos(30 degrees) = 92 N. Therefore, the tension in the rope is 92 N.

Explanation

When the rope makes an angle of 30 degrees with the horizontal, the tension in the rope can be calculated using the formula Tension = Force / Cosine(angle). In this case, the force is 80 N and the angle is 30 degrees. Plugging these values into the formula, we get Tension = 80 N / Cos(30 degrees) = 92 N. Therefore, the tension in the rope is 92 N.

3. A stationary object of mass 2.0 kg is suspended using two strings as shown below. What is the resultant force acting on the object?

0 N

8 N

20 N

48 N

Key word here is suspended, hence not moving.

Explanation

Key word here is suspended, hence not moving.

4. A picture can be hung in four different ways using wires of equal lengths. In which orientation will the tension in the wires be maximum?

A

B

C

D

When a picture is hung using wires of equal lengths, the tension in the wires will be maximum when the picture is hung in orientation D. This is because in orientation D, the weight of the picture is distributed equally among all four wires, resulting in the maximum tension in each wire. In the other orientations, the weight of the picture is not distributed equally among the wires, leading to lower tension in some of the wires.

Explanation

When a picture is hung using wires of equal lengths, the tension in the wires will be maximum when the picture is hung in orientation D. This is because in orientation D, the weight of the picture is distributed equally among all four wires, resulting in the maximum tension in each wire. In the other orientations, the weight of the picture is not distributed equally among the wires, leading to lower tension in some of the wires.

5. A 4.0 kg flower pot is having a circumference of 50 cm is suspended by three ropes of equal lengths from the ceiling. The ropes make an angle of 60^o with the horizontal plane. Determine the tension in one of the ropes.

13.3 N

15.4 N

23.1 N

26.7 N

Treat the 3 ropes to be inclined to the vertical and make them equate to the weight of the flower pot.

Explanation

Treat the 3 ropes to be inclined to the vertical and make them equate to the weight of the flower pot.