- #1
wirefree
- 105
- 21
Question:-
A block of mass 10 kg moving with a velocity of 1 m/s collides with a spring of force constant 1000 N/m. Calculate the compression of the spring at the moment when kinetic energy of the block is equal to one-fourth of the elastic potential energy of the spring.
Attempt:-
Step 1: Determine initial Kinetic Energy of block
Step 2: Using above value of K.E., determine maximum compression of spring using Law of Conservation of Mechanical Energy
Step 3: Determine acceleration for the maximum compression using 3rd Kinematic equation
Step 4: Obtain two equations with two unknowns (v & x):
- First: v2 = u2 + 2ax (3rd Kinematic equation)
- Second: 1/4*1/2*k*x2 = 1/2*m*v2 (from question statement)
Step 5: Substitute v2 from First equation in the Second and solve 25x2 + 10x - 1 = 0 for x.
Problem:-
The above question is a 4 marks exam question which gives me 9 minutes to solve it. In addition to the 4 steps preceding it, Step 5's quadratic equation doesn't yield whole number roots. To be precise they are x=.09 & x=-.48.
There must be a shorter procedure.
Would appreciate advise.
Regards,
wirefree
A block of mass 10 kg moving with a velocity of 1 m/s collides with a spring of force constant 1000 N/m. Calculate the compression of the spring at the moment when kinetic energy of the block is equal to one-fourth of the elastic potential energy of the spring.
Attempt:-
Step 1: Determine initial Kinetic Energy of block
Step 2: Using above value of K.E., determine maximum compression of spring using Law of Conservation of Mechanical Energy
Step 3: Determine acceleration for the maximum compression using 3rd Kinematic equation
Step 4: Obtain two equations with two unknowns (v & x):
- First: v2 = u2 + 2ax (3rd Kinematic equation)
- Second: 1/4*1/2*k*x2 = 1/2*m*v2 (from question statement)
Step 5: Substitute v2 from First equation in the Second and solve 25x2 + 10x - 1 = 0 for x.
Problem:-
The above question is a 4 marks exam question which gives me 9 minutes to solve it. In addition to the 4 steps preceding it, Step 5's quadratic equation doesn't yield whole number roots. To be precise they are x=.09 & x=-.48.
There must be a shorter procedure.
Would appreciate advise.
Regards,
wirefree