Question:

A block of mass 2 kg initially at rest on a frictionless horizontal surface is acted upon by a constant horizontal force of 10 N for a duration of 5 seconds. The block then collides with a spring with a spring constant of 100 N/m and compresses the spring by a maximum of 0.2 meters before coming to a stop.

a) According to Newton's first law of motion, what can be concluded about the block's initial velocity before it collided with the spring? Explain your answer.

b) According to Newton's second law of motion, what is the acceleration of the block while it is being acted upon by the constant force?

c) Use Newton's second law of motion to determine the speed of the block immediately before it collided with the spring.

d) Use the principles of conservation of energy to calculate the maximum compression of the spring.

Answer:

a) According to Newton's first law of motion, an object at rest remains at rest or an object in motion continues to move in a straight line with constant speed unless acted upon by an external force. Since the block was initially at rest on a frictionless surface, it must have had an initial velocity of 0 m/s before it collided with the spring.

b) According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation for Newton's second law is given by:

where F is the net force, m is the mass of the object, and a is the acceleration. In this case, the net force acting on the block is 10 N, and the mass of the block is 2 kg. Therefore, the acceleration of the block can be calculated as:

So, the acceleration of the block while it is being acted upon by the constant force is 5 m/s^2.

c) Given that the block's initial velocity was 0 m/s, and using the equation of motion:

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, we can solve for the final velocity.

Since the final velocity is 0 m/s (block comes to a stop), the equation becomes:

Solving for s:

Hence, we conclude that the speed of the block immediately before it collided with the spring was 0 m/s.

d) The potential energy stored in a spring is given by the equation:

where PE is the potential energy, k is the spring constant, and x is the displacement.

Using the principle of conservation of energy, the maximum compression of the spring can be calculated by equating the initial kinetic energy of the block to the potential energy stored in the spring. Since the block comes to a stop, its initial kinetic energy is 0.

Therefore, we have:

Simplifying and solving for x:

Hence, the maximum compression of the spring is 0 meters.