When a body falls freely under gravity, then the work done by the gravity is:
Raindrops fall on the earth with certain kinetic energy on the earth. From where do they get this energy?
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.
Time rate at which work is done by a force is:
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)
There are two bodies X and Y with equal kinetic energy but different masses m and 4m respectively. The ratio of their linear momentum is:
X and Y have equal kinetic energy but their masses are m and 4m respectively.
► 1/2 m_{1}v_{1}^{2} = 1/2 m_{2}v_{2}^{2}
► mv_{1}^{2} = 4m * v_{2}^{2}
► v_{1} : v_{2} = 2 : 1
Hence the ratio of their linear momentum is:
m1v1 : m2v2 = m * 2v : 4m * v = 1 : 2
A truck moves at a steady speed on a horizontal road. What is the work done by the road on the truck?
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.
Output of a truck is 4500 J and its efficiency is 50%, the input energy provided to the truck is:
► η = work output / heat input
► η = 50% = 50/100 = 1/2
► 1/2 = 4500 / Heat input
► Heat input = 9000 J
By how much does kinetic energy increase if the momentum is increased by 20%?
The kinetic energy is given by:
KE= p^{2}/2m
So, ΔKE = 2pΔp / 2m = pΔp / m
ΔKE / KE = (pΔp/m) * (2m/p^{2}) = 2Δp / p
Since the momentum p increases by 20%, so the final momentum becomes 1.2p.
Hence, KE_{final} = (1.2p)^{2 }/ 2m = 1.44p^{2} / 2m = 1.44KE
So, % change in KE = 44%
When a body slides against a rough horizontal surface, the work done by friction is:
A machine gun fires 60 bullets per minute, with a velocity of 700 m/s. If each bullet has a mass of 50g, find the power developed by the gun.
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 motion of a body, what is the amount of work done?
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.
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