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A 1.55 block slides with a speed of 0.895 on a frictionless horizontal surface u

ID: 1964865 • Letter: A

Question

A 1.55 block slides with a speed of 0.895 on a frictionless horizontal surface until it encounters a spring with a force constant of 721 . The block comes to rest after compressing the spring 4.15 .
1. Find the spring potential energy, , the kinetic energy of the block, , and the total mechanical energy of the system, , for compressions of 0 .

2. Find the spring potential energy, , the kinetic energy of the block, , and the total mechanical energy of the system, , for compressions of 1.00 .

3. Find the spring potential energy, , the kinetic energy of the block, , and the total mechanical energy of the system, , for compressions of 2.00 .

4. Find the spring potential energy, , the kinetic energy of the block, , and the total mechanical energy of the system, , for compressions of 3.00 .

5. Find the spring potential energy, , the kinetic energy of the block, , and the total mechanical energy of the system, , for compressions of 4.00 .

Explanation / Answer

m = 1.55
v = 0.895m/s
k = 721N/m
x = 4.15 cm = 0.0415m
1. For compression of 0,
Spring potential energy = kx2/2 = 0

Kinetic energy of block = mv2/2 = 1.55*0.8952/2 = 0.6208 J

Total mechanical energy of the system =Spring potential energy+Kinetic energy of block = 0.6208 J

2. As there are no discipative forces , total energy of the system remains constant

=>Total mechanical energy of the system = 0.6208 J

=> spring potential energy = kx2/2 = 721*0.012/2 = 0.036 J

Kinetic energy of block = Total mechanical energy of the system - spring potential energy = 0.6208-0.036 = 0.585 J

3. Total energy = 0.6208 J

spring potential energy = kx2/2 = 721*0.022/2 = 0.1442 J

Kinetic energy of block = Total mechanical energy - spring potential energy = 0.6208-0.1442 = 0.4766 J

4.Total energy = 0.6208 J

spring potential energy = kx2/2 = 721*0.032/2 = 0.32445 J

Kinetic energy of block = Total mechanical energy - spring potential energy = 0.6208-0.32445 = 0.29635 J

5.Total energy = 0.6208 J

spring potential energy = kx2/2 = 721*0.042/2 = 0.5768 J

Kinetic energy of block = Total mechanical energy - spring potential energy = 0.6208-0.5768 = 0.044 J