## Tuesday, November 8, 2016

### Laws of Motion Problems with Solutions Two

We are solving a series of problems based on laws of motion. In this post we are going to deal few problems based on the concept and application of force. Force is the physical quantity that change the state of the body or at least try to change the state of the body. The force acts against the inertia of the body. Inertia is the state of the body and due to inertia, the body always wish to continue its own state of rest or motion. To change this state, we need to apply force on the body.

Problem

It is given in the problem that a bullet of known mass is moving with a speed known and it is entering into a wooden piece of depth 50 centimeter. We need to measure the average force exerted by the block on the bullet. The problem is as shown in the diagram below.

Solution

It is given in the problem that the bullet got struck in the plank and hence its final velocity is zero. The displacement of the bullet is nothing but the width of the plank and it is given in the problem. We can use third equation of motion and find the negative acceleration that the bullet gets during this process. As the mass is given in the problem, we can find the force as shown in the diagram below.

Problem

It is given in the problem that a gun can exert a force of 180 newton on the bullet and the gun can fire bullets each of mass 50 gram with a speed of one kilometer per second. We need to know how many bullets can be fired this gun in one minute. The problem is as shown in the diagram below.

Solution

We know that each bullet has some velocity and hence it can have some momentum. Momentum is the ability of a body to transfer kinetic energy to other bodies. We also know that according to Newton's second law, force can be defined as the rate of change of momentum. Each bullet has some momentum and to get the total momentum of the system, we shall multiply with the number of the bullets. Thus we can solve the problem as shown below.

Problem

It is given in the problem that two forces are acting on a body of mass 1000 kilogram and the two forces are having an angular separation of 60 degree. We need to measure the acceleration acquired by the body after ten seconds when both the forces are acting on it. The problem is as shown below.

Solution

We know that force is a vector quantity. When two forces are acting simultaneously, we can find their vector resultant using parallelogram law. Once we know the magnitude of the resultant, we can divide that force with mass so that we can get the acceleration. The solution is as shown in the diagram below.

Problem

It is given in the problem that a hot air balloon of mass M is moving up with a uniform acceleration. We had removed a portion of the mass from the balloon and it is found that the remaining part start moving with double the initial acceleration. We can assume that buoyant force is not significant and we need to know the mass that is removed from the balloon in terms of the give data. The problem is as shown in the diagram below.

Solution

In the first case there is some upward force on the balloon because of which it is moving up and the downward force is the weight of the balloon. We can find the resultant force as the force acting in the direction of motion minus force acting against the motion.

We can write the same equation even after the mass is removed from the balloon and by simplifying both the equations, we can solve the problem as shown below.

Problem

Two skaters are at a certain separation on a friction-less frozen surface and they have different masses. After some time if they have a known separation, we need to measure the distance moved by the lighter skater from his original position.

Solution

We know that when no external force is acting on a system, its moment is conserved. That is the product of mass and distance is constant. By applying that concept, we can solve the problem quite easily as shown in the diagram below.

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