Engineering Answers

1.1 The speed of a shaft increases from 93 r/min to 305 r/min with an angular acceleration of 2,4 rad/s2. How many revolutions does the shaft make during the first 3 seconds of acceleration? How many revolutions does the shaft make in the last 4.25seconds. Show all calculations[10]

1.2 A motor that runs at 1240 rev/minute is required to drive a belt at 20 m/s. What diameter belt pulley is required?[3]

Also clearly show the following values:

ωi

ωf

θ

r

d

ωf

A 350 mm diameter grinding wheel must be driven at a grinding speed (speed at circumference) if 1200 meters per minute. It takes 5 seconds to reach this speed from rest, runs at this speed for the next two minutes and then starts to decelerate uniformly, finally coming to rest after a further 30 seconds. Draw a neat angular velocity-time graph and determine how many revolutions the wheel made in total.

Also clearly show what the following values are:

ω1

θ1

θ2

θ3

θtotal

A pulley (A) diameter 300mm is accelerated by means of a belt drive from 60rpm to 240rpm during 360 revolutions. Attached by means of a belt is another pulley (B), with diameter 200mm. Calculate:

a)The angular acceleration of each pulley

b)The initial and final velocity of the smaller pulley (B) in rad/s

Also

Clearly show the values of the following:

Pulley A-ωi

Pulley A-ωf

Pulley A-αA

Pulley B-αB

Pulley B-ωi

Pulley B-ωf

A jet fighter aircraft is climbing vertically ay 120m/s when it releases a bomb that hits the ground 35seconds later. How high was the jet when the bomb was released?

A hovercraft stays off the ground by blowing air out underneath it. It can accelerate (forwards or backwards) at 0,6 m/s² by blowing air with a steering fan (backwards or forwards). If the hovercraft is moving forwards at 12 m/s and the steering fan is suddenly turned to accelerate the hovercraft backwards, calculate:

a) the velocity of the hovercraft after 2 s

b) the time it takes for the hovercraft to reach zero velocity 

c) the velocity of the hovercraft after 29 s

d) the displacement of the craft when it has zero velocity

e) the displacement of the hovercraft when it is moving backwards at 16m/s

f) Clearly show what the value of h(max),t(total) and v

State whether the hovercraft is going backwards or forwards after each question’s answer.

(Make forward direction positive and backwards direction negative)

A ball is released from a window that is 10 meters above the ground. When the ball leaves your hand, it is moving 8m/s at an angle 300 below the horizontal. Ignoring the effect of air resistance, how far horizontally from the window will the ball hit the ground?

In a court with a ceiling height of 30ft, a player throws a ball towards a wall that is 80ft away. If the ball was released from height of 5ft from the floor and has initial velocity of 55 ft/s, what is the highest point at which the ball could hit the wall?

A baseball player hits a ball such that as it leaves the bat, it has speed of 40 meters per second and has an angle of 440. What is the time that the ball reaches the highest point of its flight?

A car is driving at speed of 80 mph in a circular track with a radius of 1500 ft. The driver applied brake to decelerate the car and after 6 seconds, the speed decreases to half the original speed. What is the acceleration of the car at the instant after the brakes have been applied? At ft/s2

A car has an increasing speed at rate of 1.5m/s2 as it rounds a curve. What is the radius of curvature at a point when the speed of the car is 60kph and the magnitude of the total acceleration is 4m/s2?