A marble block of mass 2 kg lying on ice when given a velocity of 6 m/...
Given information:
- Mass of marble block (m) = 2 kg
- Initial velocity (u) = 6 m/s
- Time taken to stop (t) = 10 s
Calculating acceleration:
The marble block is brought to rest by friction. We can use the equation of motion to find the acceleration (a) of the block.
The equation of motion is given by:
v = u + at
Since the final velocity (v) is 0 m/s (as the block comes to rest), we can rewrite the equation as:
0 = 6 + a * 10
Solving for acceleration:
a = -6/10
a = -0.6 m/s² (negative sign indicates deceleration)
Calculating frictional force:
Frictional force (f) can be calculated using Newton's second law of motion:
f = ma
Substituting the values:
f = 2 * (-0.6)
f = -1.2 N (negative sign indicates opposite direction to the motion)
Calculating coefficient of friction:
The coefficient of friction (μ) is defined as the ratio of the frictional force to the normal force (N) between two surfaces:
μ = f / N
However, in this case, the normal force cancels out, as the block is on a horizontal surface. Therefore, the coefficient of friction can be calculated as:
μ = f
Substituting the value of frictional force:
μ = -1.2 N
The coefficient of friction cannot be negative, so we take the absolute value:
μ = 1.2 N
Since the options given do not match the calculated value, it appears that there may be an error in the options provided. Therefore, the correct answer cannot be determined from the given options.