A moving 1.60 kg block collides with a horizontal spring whose spring constant is 480 N/m.
The block compresses the spring a maximum distance of 12.50 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.480.
What is the work done by the spring in bringing the block to rest?
I got 4.69J but it says its wrong. I sum up work done by friction plus work by spring
I will do more than you asked because I am sure there are more parts
weight = m g = 1.6*9.81 = 15.7 N
friction force = .48*15.7 = 7.53 N
work done by friction = 7.53*.125
= .942 Joules
work done by spring = (1/2)(480)(.125^2)
= 3.75 J (ANSWER YOU ASKED FOR)
total work done by friction and spring = .942+3.75 = 4.69 Joules (LOL, what you said but that is total not spring(
so
(1/2) m v^2 = 4.69 before crash
I think there something wrong with the quiz, cuz it tells me its wrong. I tried 3.75N (work by spring) and also total work done. It shouldnt be, I got the 2 other questions right. Still, thank you.
To find the work done by the spring in bringing the block to rest, we first need to calculate the work done by the friction force. Then we can subtract this value from the total work done on the block to get the work done by the spring.
Let's break down the problem into steps:
Step 1: Calculate the work done against friction.
The work done by friction can be determined by multiplying the friction force by the displacement of the block. The friction force can be calculated as the coefficient of kinetic friction multiplied by the normal force acting on the block. In this case, the normal force is equal to the weight of the block, which is the mass of the block multiplied by the acceleration due to gravity (9.8 m/s^2).
Friction force = coefficient of kinetic friction * normal force
Normal force = mass of the block * acceleration due to gravity
Step 2: Calculate the work done by the spring.
The work done by the spring can be determined using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Force exerted by the spring = spring constant * displacement of the spring
Step 3: Calculate the total work done on the block.
The total work done on the block can be found by summing up the work done by friction and the work done by the spring.
Total work = work done by friction + work done by the spring
Now, let's plug in the given values into the above calculations:
Step 1: Calculate the work done against friction.
Normal force = mass of the block * acceleration due to gravity
Normal force = 1.60 kg * 9.8 m/s^2
Friction force = coefficient of kinetic friction * normal force
Friction force = 0.480 * (1.60 kg * 9.8 m/s^2)
Step 2: Calculate the work done by the spring.
Displacement of the spring = 12.50 cm = 0.125 m
Force exerted by the spring = spring constant * displacement of the spring
Force exerted by the spring = 480 N/m * 0.125 m
Step 3: Calculate the total work done on the block.
Total work = work done by friction + work done by the spring
Finally, subtract the work done by friction from the total work to get the work done by the spring:
Work done by the spring = Total work - Work done by friction
This should give you the correct answer.