When a body falls freely under gravity, then the work done by the gravity is:
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 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
Ram and Sham together can complete a vocation in 8 days. Ram can do likewise work all alone in 12 days. To what extent will sham take to carry out the occupation without anyone else's input?
► (Ram + Sham)'s 1 day work = 1 / 8
► Ram 1 day work = 1 / 12
► Sham 1 day work = (1 / 8 - 1 / 12) = 1 / 24
∴ Sham alone can finish the work in 24 days.
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.
Which of the following is not a unit of energy?
By how much does kinetic energy increase if the momentum is increased by 20%?
The kinetic energy is given by:
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, KEfinal = (1.2p)2 / 2m = 1.44p2 / 2m = 1.44KE
So, % change in KE = 44%
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)
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
When a body slides against a rough horizontal surface, the work done by friction is: