Answer:
Step-by-step explanation:
We can use the work-energy principle to solve this problem. The work-energy principle states that the work done on an object is equal to the change in kinetic energy of the object.
We can begin by finding the spring constant (k) of the spring. The spring constant is the force required to compress a spring by a certain distance. We can use the information given to us in the problem to find the spring constant:
k = F / x = 334 N / 0.024 m = 13,916.67 N/m
Now we can use the spring constant, the compression distance (3.5 cm) and the mass of the block (1.15 kg) to find the work done on the block as it compresses the spring:
work = 1/2 * k * x^2 = 1/2 * 13,916.67 N/m * (0.035 m)^2 = 97.4 J
Since the block is released from rest, its initial kinetic energy is zero. So, the work done on the block as it compresses the spring is equal to its final kinetic energy.
We know that the block slides down on a frictionless incline, so we need to consider the work done by gravity on the block during its motion. The work done by gravity is given by the equation:
work = force * distance * cos(theta)
where force is the force of gravity acting on the block, distance is the distance the block slides down the incline and theta is the angle of the incline with the ground.
force = m * g , where m = 1.15 kg and g = 9.8 m/s^2
distance = s
theta = 35°
substituting the values
work = (1.15 kg * 9.8 m/s^2) * s * cos(35°)
Now we can add the work done by gravity to the work done by the spring to find the total work done on the block.
work = 97.4 J + (1.15 kg * 9.8 m/s^2) * s * cos(35°) = 97.4 J + (11.37 N) * s * cos(35°)
Now we can solve for s, the distance the block travelled.
s = (97.4 J) / (11.37 N * cos(35°))
The final answer will be in meters.