A four-bar linkage system is shown below. The first link, a, is an input link (crank) of length 1m. The second link, b, is a coupler link of length 2m. The third link, c, is an output link of length 3m. The fourth link, d, is the fixed link (ground) of length 4m.

The angular position of the output link (θ₄) of a four-bar linkage corresponding to the angular position of the input link (θ₂) can be computed using Freudenstein’s equation:

Using the modified secant method to determine the value of θ₄ when θ₂ = 40ᵒ. With an initial guess of x_i = 100ᵒ, perturbation δ = 0.01 and precision of 0.0001.

A four-bar linkage system is shown below. The first link, a, is an input link (crank) of length 1m. The second link, b, is a coupler link of length 2m. The third link, c, is an output link of length 3m. The fourth link, d, is the fixed link (ground) of length 4m.

The angular position of the output link (θ₄) of a four-bar linkage corresponding to the angular position of the input link (θ₂) can be computed using Freudenstein’s equation:

Using the Secant method to determine the value of θ₄ when θ₂ = 40ᵒ. With an initial guesses of x_i = 100ᵒ and x_i-1 = 110ᵒ, and precision of 0.0001.

For some functions open methods (such as Newton-Raphson and secant methods) find a root faster than bracketing methods. But for some other functions open methods could take very long or never converge to a root. Explain why this happens with the open methods but not with the bracketing methods. 

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A four-bar linkage system is shown below. The first link, a, is an input link (crank) of length 1m. The second link, b, is a coupler link of length 2m. The third link, c, is an output link of length 3m. The fourth link, d, is the fixed link (ground) of length 4m.

The angular position of the output link (θ₄) of a four-bar linkage corresponding to the angular position of the input link (θ₂) can be computed using Freudenstein’s equation:



Using the Newton-Raphson method to determine the value of θ₄ when θ₂ = 40ᵒ. With an initial guess of x_i = 100ᵒ and precision of 0.0001.

The derivative of the Freudenstein equation is

A vehicle is travelling at 72 km/h (20 m/s) when the driver sees a couple walk out on to the road 20m ahead (d=20m). The driver brakes immediately and stops just in time to avoid impact (i.e braking distance is 20m). The vehicle decelerates at a constant, gradual rate without skidding.

If the mass of the car is 1000kg, what was the work and power required to decelerate the vehicle?

The shaft of a turbine has a moment of inertia of 14 kg m² about its centre, while each of the three turbine blades has a moment of inertia of 2 kg m², relative to the centre of rotation of the turbine. What torque must be applied to the turbine to achieve an angular acceleration of 2 rad/sec²?

Give your answer in N.m to at least 2 significant figures

A small child of mass 35 kg is sitting on a playground swing. The child's centre of mass is 1.5 metres from the pivot point of the swing. If the child is pushed by an adult applying 110 N of force as shown in the diagram, what torque will be applied to the child?

Assume the pushing action is perpendicular to the chain, that the chain remains taut, and that the force is applied instantaneously. Give your answer in N.m to the nearest whole number.

A unicylist is riding down the Princes Highway at a constant velocity. The free body diagram of his wheel is shown below. The rider is applying a torque (360 N.m) to the 0.5 m radius wheel which is opposed by the friction force Fr. If the coefficient of static friction is 0.6, and the coefficient of kinetic friction is 0.2, what is the combined mass of the wheel and rider?

Assume the wheel is not slipping (but would slip if any additional torque were applied), and assume gravitational acceleration is 9.81 m/s². Give your answer in kg to the nearest whole number.

A similar situation occurs, but this time, the adult pushes downwards on an angle with the same force.

Assume the pushing action is at an angle of 60 degrees from the horizontal, that the chain remains taut, and that the force is applied instantaneously. Find the applied torque, and give your answer in N.m to the nearest whole number.