Question

A block of mass m = 3.5 kg is attached to a spring with spring constant k = 990 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 22° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.12. In the initial position, where the spring is compressed by a distance of d = 0.19 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero.

what is the blocks initial mechanical energy in joules? If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion

Answer 1

The block's initial mechanical energy is zero joules. The distance the block will travel before coming to rest can be determined using the conservation of mechanical energy equation.

Step-by-step explanation:

The block's initial mechanical energy can be calculated by summing up the potential energy and the kinetic energy. In this case, the block is at its lowest position, so the potential energy is zero. The initial kinetic energy can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the block and v is its velocity. Since the block is initially at rest, its velocity is zero, so the initial kinetic energy is also zero. Therefore, the block's initial mechanical energy is zero joules.

When the spring pushes the block up the incline, the block gains potential energy and loses kinetic energy due to the work done by the spring and the friction. The distance the block will travel before coming to rest can be determined by the conservation of mechanical energy equation, which states that the initial mechanical energy is equal to the final mechanical energy. In this case, the initial mechanical energy is zero, so the final mechanical energy must also be zero when the block comes to rest. By using the work-energy theorem and calculating the work done by the spring and the work done by friction, the distance L can be found.