Work, Energy and Power Test - 11

• If a force acting on a body has a component in the direction of displacement, then the work done by the force is positive.
• Hence when a body falls freely under the influence of gravity the work done by gravity is positive.

Every object that tends to fall or does fall on earth's surface does have a gravitational acceleration which is possessed by them due to their gravitational potential energy.

We know that Work done, W = F.s
where F is force and s is displacement due to that force.
Thus rate of work done is: 

dW/dt = d(F.s)/dt

So as F is constant we get, 
dW/dt = F.d(s)/dt = F.v = P (Power)

X and Y have equal kinetic energy but their masses are m and 4m respectively.
► 1/2 m₁v₁² = 1/2 m₂v₂²  
► mv₁² = 4m * v₂²  
► v₁ : v₂ = 2 : 1
Hence the ratio of their linear momentum is:
m1v1 : m2v2 = m * 2v : 4m * v = 1 : 2

The work done is zero because while the truck does have a displacement over time, the force of the road (the normal force) is perpendicular and so the dot product of the two is zero.

► η = work output / heat input​
► η = 50% = 50/100 = 1/2
► 1/2 = 4500 / Heat input
► Heat input = 9000 J

The kinetic energy is given by: 

KE= p²/2m

So, ΔKE = 2pΔp​ / 2m = pΔp / m​
ΔKE / KE ​= (pΔp/m)​ * (2m/p²)​ = 2Δp / p
Since the momentum p increases by 20%, so the final momentum becomes 1.2p.
Hence, KE_final​ = (1.2p)² / 2m​ = 1.44p² / 2m​ = 1.44KE
So, % change in KE = 44%

• If a force acting on a body has a component in the opposite direction of displacement, the work done is negative.
• So when a body slides against a rough horizontal surface, its displacement is opposite to that of the force of friction. The work done by the friction is negative.

Mass of the bullets = 60×50 = 3000g = 3kg
v = 700m/s t = 1min = 60s
Power = W/t = (Kinetic energy)/t = 12250W.

If a force acts perpendicular to the direction of a body, the amount of work done is zero because there is no displacement in the direction of a force.