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Question

Which requires more work, lifting a 6 kg rock to a height of 9 m without accelerating, or accelerating the same rock horizontally from rest to a speed of 15m/s? Work to lift the rock? Work to accelerate rock?

Answer 1

Here,

mass of the rock = 6 kg
height, h = 9 m
gravitational acceleration, g = 9.8 m/s^2
initial speed, u = 0 m/s
final speed, v = 15 m/2

Work done to lift the rock without accelerating, W1 = ?
Work done to accelerate it horizontally, W2 = ?

When lifting,
W1 = mgh
or, W1 = 6 * 9.8 * 9
so, W1 = 529.2 J

Work to lift the rock = 529.2 J

When accelerating horizontally,
W2 = change in kinetic energy
= 1/2mv^2 - 1/2mu^2
= 1/2 * 6 * 15^2 - 0 [ because u = 0 m/s ]
= 675 J
so, W2 = 675 J

Work to accelerate the rock = 675 J

Clearly W2 > W1

So, accelerating the rock horizontally requires more work.

Hope this was helpful.

Answer 2

Work = change in energy.

When lifting, you increase the potential energy, U = m*g*h, wher g= Acc due to gravity, 9.8 m/s^2

When accelerating a body, your increasing kinetic energy from 0 to 0.5*m*(v^2) where v is the final velocity.

Do the math, where the change in energy is higher, more work is done

Answer 3

lifting requires more work;