Question

An electric lift can raise a 500 kg mass a distance of 10 m in 5s. what is the power of the lift?

Answer 1

My answer number 0901

Explanation : A crane can lift 5,000 kg of mass to the height of 10 m in 10 seconds. What is its power?

The power (P) is equal to the work done (W) divided by the time (t)

P=Wt

The work done (W) is equal to the force (F) times the distance (d)

W=F∗d

The force (F) is equal to mass (m) times acceleration (a)

F=m∗a

Putting it together, it is: W=m∗a∗d

Easy way to remember: Work makes me mad .

which means

P=m∗a∗dt

Units to use:

Power in Watts (W) , where 1watt=1 J/s

Work done in Joules (J) , where 1 J=1 N∗m=1 kg∗(m/s2)∗m=1 kg∗m2/s2

Time in seconds (s)

Force in Newtons (N) , where 1 N=1 kg∗m/s2

Distance in meters (m)

Mass in kilograms (kg)

Acceleration in meters per square-second (m/s2)

Here we are given:

Mass is 5000 kg → m=5000

Acceleration → since the force is applied VERTICALLY (because of the words “lift” and “height”), the acceleration is also vertical. Neglecting air resistance, the vertical acceleration is gravity, whose acceleration on Earth is 9.807 m/s2 . Therefore, a=9.807

Distance (the vertical height) is 10 m → d=10

Time is 10 seconds → t=10

We need to find: Power: P= ?

Plug in m=5000, a=9.807, d=10, t=10 into P=m∗a∗dt and solve for P

P=5000∗9.807∗1010

P=5000∗9.807

P=49 035

Therefore, the power is approximately 4.90×104 watt , or approximately 65.7 hp (see conversion below)

Let’s convert 49 035 watt into horse-power, where 1 hp=746 watt (approximately).

49 035 watt ∗ 1 hp746 watt=49 035∗1 hp746=49 035 hp746=65.7306 hp

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