A 0.40kg block is held against a compressed spring of stiffness 68.2N/m and compression 0.64m parallel to a 24 degree incline that is 1.27m long. The coefficient of kinetic friction between the block and the incline is 0.34. The external force holding the block against the compressed spring is then removed, and the compressed spring pushes the block up the incline from rest. What is the work done by gravity on the block along the length of the incline?
What is the work done by kinetic friction along the length of the incline?
What is the work done by the spring while the block is in contact with it?
What is the speed with which the block leaves the incline?
To find the work done by gravity on the block along the length of the incline, we'll need to consider the gravitational force acting on the block and then calculate the work done by this force.
First, let's determine the gravitational force acting on the block. The gravitational force can be calculated using the formula:
F_gravity = m * g
Where:
m = mass
g = acceleration due to gravity (approximately 9.8 m/s²)
Given that the mass of the block is 0.40 kg, we can calculate the force of gravity as follows:
F_gravity = 0.40 kg * 9.8 m/s²
F_gravity = 3.92 N
Now that we have the gravitational force, we can determine the work done by this force along the length of the incline. Work is equal to the dot product of the force and the displacement vector. In this case, the displacement vector is parallel to the incline.
The formula to calculate work is:
Work = F * d * cos(θ)
Where:
F = force
d = displacement
θ = angle between the force and displacement vectors
In this case, the angle between the force of gravity and the displacement vector is the incline angle, which is given as 24 degrees.
The length of the incline is given as 1.27 m, and the force of gravity is 3.92 N. Plugging in the values into the formula, we can calculate the work done by gravity as follows:
Work = 3.92 N * 1.27 m * cos(24°)
Work = 4.981 J
Therefore, the work done by gravity on the block along the length of the incline is approximately 4.981 Joules.