Question
The work done by a person to push a 10-kg box up an incline of 1 meters high is 150 J. The length of the incline is 5 meters. What is the energy gain of the box? [Take g = 10 m/s^2.]
a) 200 J b) 150 J c) 100 J d) 50 J.
Answer
Both answers b) and c) are right depending on the conditions which you have not given and taking g = 10 m/s^2. Of course, the probability of 150 J being right is high.
( i ) If there is no loss due to friction, then 150 J is the right answer. Of this 100 J will go to increase its potential energy and the balance 50 J will increase its kinetic energy due to which it will have velocity at the end.
( ii ) If there is friction, then a MAXIMUM of 50 J or less depending upon the coefficient of friction may be lost. If 50 J is lost, then the body will be left with a gain of 100 J. The probability of this is extremely low, practically zero, as this will require that the body is being pushed up with a force negligibly more than the sum of weight and the maximum frictional force. As a result its acceleration will be negligible and so the gain of kinetic energy. But this will take it infinite time to go up. It is possible that the frictional force may be less than the applied force. Then body will lose less than 50 J against friction. Suppose it loses 30 J to overcome friction. Then its energy at the end will be 120 J of which 100 J will be in the form of potential energy and the rest 20 J will be in the form of kinetic energy.
Let me elaborate. Suppose you want to lift a body of 10 kg vertically up a height of 1 m. You cannot do this unless you apply a force upwards which is more than its weight. Any force more than its weight can lift it up. Its weight is 10 x 9.8 = 98 N. Now if a force of 130 N is applied, work done will be 130 J of which 98 J will increase its P.E. and 32 J will increase its K.E. The total energy of the body will be 130 J. The velocity of the body at the end is given by 32 = (0.2)(10)v^2 => v = 4 m/s^2. If one wants the gain in energy of the body = 98 J, one will have to apply a force negligibly more than its weight, i.e., 98 N, but then the net force upwards will be neglibible resulting in negligible acceleration and negligible gain in K.E. The process is infinitesimally slow. Such a process is called a reversible process. Reversible process is an ideal situation defined in thermodynamics and is energy efficient.
The work done by a person to push a 10-kg box up an incline of 1 meters high is 150 J. The length of the incline is 5 meters. What is the energy gain of the box? [Take g = 10 m/s^2.]
a) 200 J b) 150 J c) 100 J d) 50 J.
Answer
Both answers b) and c) are right depending on the conditions which you have not given and taking g = 10 m/s^2. Of course, the probability of 150 J being right is high.
( i ) If there is no loss due to friction, then 150 J is the right answer. Of this 100 J will go to increase its potential energy and the balance 50 J will increase its kinetic energy due to which it will have velocity at the end.
( ii ) If there is friction, then a MAXIMUM of 50 J or less depending upon the coefficient of friction may be lost. If 50 J is lost, then the body will be left with a gain of 100 J. The probability of this is extremely low, practically zero, as this will require that the body is being pushed up with a force negligibly more than the sum of weight and the maximum frictional force. As a result its acceleration will be negligible and so the gain of kinetic energy. But this will take it infinite time to go up. It is possible that the frictional force may be less than the applied force. Then body will lose less than 50 J against friction. Suppose it loses 30 J to overcome friction. Then its energy at the end will be 120 J of which 100 J will be in the form of potential energy and the rest 20 J will be in the form of kinetic energy.
Let me elaborate. Suppose you want to lift a body of 10 kg vertically up a height of 1 m. You cannot do this unless you apply a force upwards which is more than its weight. Any force more than its weight can lift it up. Its weight is 10 x 9.8 = 98 N. Now if a force of 130 N is applied, work done will be 130 J of which 98 J will increase its P.E. and 32 J will increase its K.E. The total energy of the body will be 130 J. The velocity of the body at the end is given by 32 = (0.2)(10)v^2 => v = 4 m/s^2. If one wants the gain in energy of the body = 98 J, one will have to apply a force negligibly more than its weight, i.e., 98 N, but then the net force upwards will be neglibible resulting in negligible acceleration and negligible gain in K.E. The process is infinitesimally slow. Such a process is called a reversible process. Reversible process is an ideal situation defined in thermodynamics and is energy efficient.
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