A 13.0kg block slides 5.00m down a frictionless surface inclined 31.0° above the horizontal, before being stopped by an originally unstretched spring of spring constant k=346N/m secured to the inclined surface. Find the maximum compression of the spring.
(13x9.81xsin31x5)/(0.5x346)
=1.89
Is this correct?
well, it slid more than 5 meters if it squished the spring after 5 meters. Note they used the wording "before being stopped".
falls 5+x meters
squished x meters
so
loss of gravitational potential energy = m g (5+x)/sin 31
=
gain of spring potential energy = (1/2) k x^2
I am getting 1.17m, is that correct?
Do not have calculator but
13 (9.81) (1.17+5 ) = about 780
.5 * 350 * 1.17^2 = about 175*1.3
nope
13 * 9.81 * 5/.515 + 13*9.81 x/.515 = .5 * 346 x^2
173 x^2 - 265 x - 1247 = 0
https://www.mathsisfun.com/quadratic-equation-solver.html
3.56
To find the maximum compression of the spring, we can use the principles of conservation of mechanical energy.
First, we need to determine the initial potential energy of the block at the top of the incline. The potential energy can be calculated by multiplying the mass of the block (13.0 kg) by the acceleration due to gravity (9.81 m/s²) and the height of the incline (5.00 m), multiplied by the sine of the angle of inclination (31.0°).
Potential Energy = mass × gravity × height × sin(angle)
= 13.0 kg × 9.81 m/s² × 5.00 m × sin(31.0°)
≈ 615 J
Next, we know that this potential energy is converted to the maximum potential energy stored in the spring when it is fully compressed. This potential energy can be calculated using the formula:
Potential Energy = (1/2) × k × compression²
Where k is the spring constant (346 N/m) and compression is the maximum compression of the spring that we want to find.
Therefore, we can rearrange the formula to solve for compression:
compression² = (2 × Potential Energy) / k
= (2 × 615 J) / 346 N/m
= 1.76 m²
Finally, we take the square root of the result to find the maximum compression of the spring:
compression ≈ √(1.76 m²)
≈ 1.33 m
So, the correct answer for the maximum compression of the spring is approximately 1.33 m. Therefore, the calculation you provided of 1.89 m is not correct.