Effects of forces

Formula: Extension = New Length - Original Length
Working: Extension = 17.0 cm - 15.0 cm = 2.0 cm
Answer: 2.0 cm
Explanation: The extension is the change in length of the spring due to the applied force (the weight).

1. The rubber band might increase in length (stretch). This is a change in size.
2. The rubber band might become thinner (decrease in cross-sectional area). This is a change in shape.

These changes are due to the force applied to the rubber band.

Extension = New Length - Original Length
Extension = 18.0 cm - 15.0 cm = 3.0 cm
Extension = 3.0 cm / 100 = 0.03 m

*Explanation: The extension is the difference between the spring's new length under load and its original length. Converting centimetres to metres requires dividing by 100.*

1. Apparatus: Spring, ruler, clamp stand, weights (known masses), weight hanger.
2. Set Up: Clamp the spring vertically using the clamp stand.
3. Measure Original Length: Record the initial length of the spring without any load.
4. Add Load: Add weights to the weight hanger one at a time. For each weight added, record the new length of the spring.
5. Calculate Extension: For each weight, calculate the extension by subtracting the original length from the new length.
6. Repeat: Repeat the process for several different loads.
7. Plot Graph: Plot a graph of load (on the y-axis) against extension (on the x-axis).

Resultant force = Forward force - Resistive force
Resultant force = 4500 N - 700 N
Resultant force = 3800 N

The resultant force is the overall force acting on an object after considering all individual forces. It's the net effect of all forces combined.

Determining the resultant force is important because it indicates the net effect of all forces acting on the vehicle. The magnitude and direction of the resultant force directly determines the vehicle's acceleration (or deceleration) according to Newton's Second Law (F = ma). Knowing the resultant force allows us to predict the motion of the vehicle; a zero resultant force means the vehicle is either at rest or moving at constant velocity. A non-zero resultant force indicates the vehicle is accelerating or decelerating.

The car is travelling at a constant speed in a straight line, therefore the resultant force is zero. This means the driving force and the resistive force are equal and opposite.

Resistive force = Driving force = 500 N

The hockey puck will come to rest because of a resultant force acting on it. Even though the ice is smooth, there is still friction (a resistive force) between the puck and the ice. This friction opposes the motion of the puck. Because there are no other forces to balance the friction, the resultant force is non-zero, and this causes the puck to decelerate until it stops.

1. Calculate acceleration:
* *F* = *ma*
* 0.5 N = 2.0 kg * *a*
* *a* = 0.25 m/s²

2. Calculate the change in velocity:
* *v* = *u* + *at*
* *v* = 0 + 0.25 m/s² * 4.0 s
* *v* = 1.0 m/s

Answer: The magnitude of the car's change in velocity is 1.0 m/s. The resultant force causes an acceleration perpendicular to the initial velocity, changing the direction and hence the velocity of the car.

1. Change in speed: The resultant force could cause the bicycle to speed up (increase its velocity) or slow down (decrease its velocity).

2. Change in direction: The resultant force could cause the bicycle to change its direction, even if its speed remains constant. Note: A change in direction *is* a change in velocity, even if the speed is constant.

Formula: k = F/x
Substitution: k = 5.0 N / 0.20 m
Answer: k = 25 N/m
Explanation: The spring constant is the force required per unit extension. A larger spring constant indicates a stiffer spring.

The spring constant of 40 N/m means that a force of 40 N is required to extend (or compress) the spring by 1 meter.

The approximate limit of proportionality is 4N.

Explanation: Up to 4N, the extension increases proportionally with the load (for every 1N increase in load, the extension increases by 0.5cm). After 4N, the extension only increases by 0.4cm. This indicates that the relationship is no longer linear, and the limit of proportionality has been exceeded.

F = ma
F = 800 kg * 2.5 m/s²
F = 2000 N
The resultant force is 2000 N. This force causes the car to accelerate.

According to Newton's Second Law (F=ma), an object accelerates only if there is a resultant force acting on it. If the forces are balanced, the object will either remain at rest or continue moving at a constant velocity. Therefore, a resultant force is necessary for acceleration to occur.

Formula: F = mv²/r

Initial: 0.8 = (0.2 * v₁²)/0.5 => v₁² = (0.8 * 0.5)/0.2 = 2 => v₁ = √2 ≈ 1.41 m/s

Final: 1.6 = (0.2 * v₂²)/0.5 => v₂² = (1.6 * 0.5)/0.2 = 4 => v₂ = √4 = 2 m/s

Answer: The new speed will be 2 m/s. Increasing the force increases the speed, keeping the radius constant.

The satellite's orbital radius will decrease. Since the centripetal force (gravitational force in this case) is directly proportional to the square of the speed and inversely proportional to the radius (F = mv²/r), if the force increases while the speed and mass remain constant, the radius must decrease to maintain the equality. A stronger gravitational pull forces the satellite into a tighter orbit.

Frictional force = Applied Force (since constant speed, forces are balanced)
Frictional Force = 5.0 N

Explanation: When an object moves at a constant speed, the net force acting on it is zero. Therefore, the frictional force must be equal and opposite to the applied force.

As the tires roll on the road surface, there is a force of friction between the tire and the road. This friction opposes the motion of the tire. The constant rubbing between the tire and the road converts some of the kinetic energy into thermal energy due to the work done by the frictional force. This thermal energy causes the tires to heat up.

Resultant force = Weight - Drag Force
Resultant force = 0.45 N - 0.2 N
Resultant force = 0.25 N

Explanation: The resultant force is the vector sum of all forces acting on the ball. Since weight acts downwards and drag upwards, we subtract drag from weight.

The stone experiences air resistance (drag) as it falls through air and water. Water is more viscous than air; thus the drag force exerted by water on the stone is greater than the drag force exerted by air. The resultant force on the stone is smaller when falling in water, thus it accelerates less and falls slower than when falling in air.

Air resistance = Driving Force (since constant velocity, forces are balanced)
Air resistance = 800 N

Explanation: At constant velocity, acceleration is zero. Therefore, the net force is zero. This means the air resistance must be equal and opposite to the driving force.

The parachute increases the surface area exposed to the air. This significantly increases the air resistance (drag force) acting upwards on the sky diver. The increased air resistance is now greater than the sky diver's weight (force due to gravity). This produces a resultant upward force, causing the sky diver to decelerate (slow down).