A block of mass 20gm moves along a smooth surface at a speed of 5m/s and collides with a spring constant 20N/m.what will be the maximum compression of a spring?
To find the maximum compression of the spring, we need to use the principles of energy conservation. Here's how we can calculate it:
1. Determine the initial kinetic energy of the block:
The initial kinetic energy (KE) of the block can be calculated using the formula:
KE = 0.5 * mass * velocity^2
Given:
Mass = 20 g = 0.02 kg (since 1 kg = 1000 g)
Velocity = 5 m/s
Substitute these values into the formula:
KE = 0.5 * 0.02 kg * (5 m/s)^2
= 0.5 * 0.02 kg * 25 m^2/s^2
= 0.5 * 0.02 * 25 Joules
= 0.25 Joules
Therefore, the initial kinetic energy of the block is 0.25 Joules.
2. Determine the potential energy stored in the spring:
The potential energy stored in the spring (PE) is given by:
PE = 0.5 * k * x^2
Given:
Spring constant (k) = 20 N/m
Maximum compression (x) = ?
Since the block comes to rest at maximum compression, all the initial kinetic energy is converted into potential energy stored in the spring.
Equating the initial kinetic energy to the potential energy stored in the spring:
0.25 J = 0.5 * 20 N/m * x^2
Simplify the equation:
0.25 J = 10 N/m * x^2
Divide both sides by 10 N/m:
0.025 m^2 = x^2
Take the square root of both sides:
x = √(0.025 m^2)
Therefore, the maximum compression of the spring is approximately 0.158 m (or 15.8 cm).
Hence, the maximum compression of the spring is 0.158 m (or 15.8 cm).