Effects Of Forces

A force may produce a change in the size of an object; a force may produce a change in the shape of an object.

The two forces act in opposite directions along the spring; the forces are equal in magnitude; therefore the resultant force is zero; there is no acceleration, but the spring extends because the forces pull it apart, changing its size.

Hang the spring from a clamp stand with a pointer attached to its lower end; place a metre rule vertically beside the spring; record the initial position of the pointer (original length); add a known mass to the weight hanger and record the new pointer position; calculate extension by subtracting the original length from the new length; repeat for increasing loads; plot load on the y-axis against extension on the x-axis.

The extension for 4.0 N is 16.0 − 12.0 = 4.0 cm; the extension for 8.0 N is 20.0 − 12.0 = 8.0 cm; doubling the load doubles the extension; therefore extension is directly proportional to load; the spring is within its proportional region and behaves as an elastic solid obeying a linear load–extension relationship.

The spring constant is the force per unit extension.

Finding the extension for 5.0 N Equation used: spring constant equation, rearranged for extension $$k=\frac{F}{x}$$ Rearranging for $x$: $$x=\frac{F}{k}$$ Given: $$F=5.0\text{ N}$$ $$k=200\text{ N/m}$$ Substituting: $$x=\frac{5.0}{200}$$ $$x=0.025\text{ m}$$ Predicting the extension for 10.0 N The spring is within its limit of proportionality, so extension is directly proportional to force. Doubling the force from 5.0 N to 10.0 N doubles the extension. $$x=2\times 0.025$$ $$x=0.050\text{ m}$$

Taking the direction of the 8.0 N force as positive: $${F}_{\text{resultant}}=8.0-3.0$$ $${F}_{\text{resultant}}=5.0\text{ N in the direction of the 8.0 N force}$$

Taking rightward as positive: $${F}_{\text{resultant}}=12-5-3$$ $${F}_{\text{resultant}}=+4.0\text{ N}$$ The resultant force is 4.0 N to the right. Because the resultant force is not zero, the box accelerates to the right.

The object continues at constant speed in a straight line when the resultant force acting on it is zero.

The car does not accelerate because the resultant force is zero; friction and air resistance provide a backward force equal to the forward force of 2000 N; the forces are balanced, so there is no change in velocity; by Newton’s first law, the car continues at constant speed in a straight line.

A resultant force can change the speed of the object; a resultant force can change the direction of motion of the object.

Velocity is speed in a stated direction; although the speed remains constant, the direction of motion changes continuously as the ball follows a circular path; therefore the velocity changes because the direction component of velocity is changing; a resultant force must be acting towards the centre of the circle to cause this change in direction.

Solid friction is the force between two surfaces that may impede motion and produce heating.

Friction acts between the block and the table surfaces; friction opposes the motion of the block; energy is transferred from the kinetic store to the thermal store of the surfaces; the increase in thermal energy causes the temperature of both surfaces to increase.

Similarity: both act in the opposite direction to the motion of the object / both oppose motion. Difference: drag in a liquid is generally greater than drag in a gas at the same speed because liquids are denser than gases.

Initially the weight is greater than the air resistance, so there is a resultant downward force; this resultant force causes the skydiver to accelerate downward; as speed increases, air resistance increases; eventually air resistance equals the weight; the resultant force becomes zero; by Newton’s first law, the skydiver continues at constant speed (terminal velocity) because no resultant force acts.

Acceleration is the change in velocity per unit time.

Step 1: Finding the acceleration Equation used: definition of acceleration $$a=\frac{\Delta v}{t}$$ Given: $$\Delta v=20-0=20{\text{ m s}}^{-1}$$ $$t=8.0\text{ s}$$ Substituting: $$a=\frac{20}{8.0}$$ $$a=2.5{\text{ m s}}^{-2}$$ Step 2: Finding the resultant force The acceleration of 2.5 m s⁻² from Step 1 is used as a given value. Equation used: Newton’s second law $$F=m a$$ Given: $$m=1200\text{ kg}$$ $$a=2.5{\text{ m s}}^{-2}$$ Substituting: $$F=1200\times 2.5$$ $$F=3000\text{ N in the direction of motion}$$

The force is directed towards the centre of the circle; it is perpendicular to the direction of motion of the object.

The speed of the ball decreases. The force in the string provides the inward (centripetal) force that keeps the ball moving in a circle. With the force and the mass kept constant, a smaller radius corresponds to a lower speed, so reducing the radius makes the ball move more slowly.