Basic Mechanics 602

If a mass of 500kg is lifted through a height of 2m, calculate the amount of work done.

Answer explanation

To calculate the work done when lifting a mass vertically:

Work Done (W) =Force (F) × Distance (d)

Since the force required to lift the object is equal to its weight, we calculate force as:

 

Force (F) = mass × gravitational field strength (g)

 

𝐹 = 500kg × 9.81m/s2 = 4905N

Now calculate the work:

 

𝑊 = 4905N × 2m = 9810 Joules

A mass of 300kg is raised through a vertical height of 8m. Calculate the amount of work done.

Answer explanation

To calculate the work done when lifting a mass vertically, use the formula:

 

Work Done (W) =Force (F) × Distance (d)

Since the force required to lift the object is equal to its weight, we calculate force as:

 

Force (F) = mass × gravitational field strength (g)

 

𝐹 = 300kg × 9.81m/s2 = 2943N

Now calculate the work:

 

𝑊 = 4900N × 8m = 23,544 Joules

Calculate the work done when a force of 750N moves an object through a horizontal distance of 15m.

Answer explanation

To calculate the work done when moving a mass horizontally, use the formula:

 

Work Done (W) =Force (F) × Distance (d)

 

Force (F) × distance (d)

 

W = 750N × 15

W = 11,250

Calculate the work done when a force of 350N moves an object through a distance of 3.7m

Answer explanation

To calculate the work done when moving a mass horizontally, use the formula:

 

Work Done (W) =Force (F) × Distance (d)

 

Force (F) × distance (d)

 

W = 350N × 3.7m

W = 1295J

Calculate the distance covered by a trolley of 51kg when the amount of work done is 1,020Nm.

Answer explanation

Since the trolley is being moved horizontally and no angle is given, assume the force equals the weight (if lifted) or the applied force.

If it’s being pushed horizontally, we need to know the force applied.
But if it's lifted, then:

F= mass × g = 51 kg×9.81m/s2 = 500.31 

Step 2: Use the formula for distance:

d=1,020 Nm / 499.8 N = 2.04 m

An object is moved across a distance of 20m in 5 seconds by a force of 50N. Calculate the power used.

Answer explanation

To calculate power, we need to use the formula:

Power = Work done / Time

First calculate the time done:

Work = Force x distance

Work = 50N x 20m = 1000J

Finally we need to calculate power:

Power = work / time

Power = 1000J / 5s = 200w

Calculate the power required to move a weight of 300N through a vertical distance of 5m in 2 seconds

Answer explanation

To calculate power, we need to use the formula:

Power = Work done / Time

First calculate the time done:

Work = Force x distance

Work = 300 x 5m = 1500J

Finally we need to calculate power:

Power = work / time

Power = 1500J / 2s = 750w

A mass of 40 litres of water is lifted through a height of 10m in 5 seconds. Calculate the power that has been used.

Answer explanation

40L Water = 40Kg

40Kg x 9.81 = 392.4Nm

392.4Nm x 10m = 3924J

3924 / 5 = 785w

Calculate the power required to raise 2.5m³ of water from a well 12.5m deep in 30 seconds.

Note: 1m³ of water = 1,000kg

Answer explanation

1m3 of water = 1000kg

2.5m3 = 2500kg

2500 x 9.81 = 24525N

24525N x 12.5m = 306,562.5J

306,562.5J / 30s = 10218.75w or 10.21Kw

An electric motor drives a pump that raises 1,000 litres of water each minute to a tank 20m above ground level. Calculate the power that the motor must provide if the pump is only 67%

Answer explanation

Since 1 litre of water has a mass of approximately 1 kg

Mass = 1,000 kg per minute

Use the formula:

E = m g h

Where:

• m = 1,000 kg

• g=9.8 m/s2 h=20 m

E= 1,000 × 9.81 × 20 = 196,200 Joules per minute

Power is energy per second, so:

Useful power output = 196,200 / 60 = 3,270w

Given the pump is only 67% efficient, the motor must supply more power than this:

Motor power = 3,270 / 0.67 = 4,880.59w or 4.88kW